20 easy SAT Nonlinear functions questions

These are the questions most test-takers get right. They are worth practising anyway: on the digital SAT the easy questions in Module 1 are what route you into the harder, higher-scoring Module 2, so dropping one costs more than it looks.

Every question below is a real item from the SAT Climb bank, tagged easy by the same difficulty model the app uses to build your practice. Pick an answer before you open the explanation.

Math · Advanced Math~5 per testEasy tier

None of these repeat the 25 hard Nonlinear functions questions, so the two pages together are 45 different questions on this one skill.

Question 1Easy

The function f is defined by f(x) = - $(x + 2)^{2} + 9$ . What is the maximum value of f(x)?

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Why B is right

The function f(x) = - $(x + 2)^{2} + 9$ is in vertex form with vertex at (-2, 9). Since the coefficient of the squared term is negative, the parabola opens downward, making the vertex a maximum. Therefore, the maximum value is 9.

Why the others are wrong

AThis uses the h-value (x-coordinate) from the vertex instead of the k-value (y-coordinate), which gives the maximum value.
CThis incorrectly negates the k-value from the vertex form, confusing the sign of the vertical shift.
DThis incorrectly subtracts the h and k values from the vertex form (9 - 2 = 7), rather than identifying k as the maximum value.

Question 2Easy

A medication in a patient's bloodstream has an initial concentration of 320 milligrams and decreases to 70% of its concentration every 6 hours. Which function models the concentration C in milligrams after t hours?

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Why C is right

The concentration decreases to 70% (multiplied by 0.7) every 6 hours, so after t hours there have been $t/6$ periods. Starting at 320 milligrams, the model is $C(t) = 320$ (0.7)^ $(t/6)$ .

Why the others are wrong

AThis incorrectly uses 6t in the exponent instead of t/6, inverting the time-period relationship.
BThis interprets 'decreases to 70%' as 'decreases by 70%' (leaving 30%), confusing retention with reduction.
DThis applies the decay factor every hour instead of every 6 hours, missing the time-period adjustment.

Question 3Easy

The function f is defined by f(x) = - $x^{2} + 10x - 21$ . What is the sum of the x-intercepts of the graph of $y = f$ (x) in the xy-plane?

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Why B is right

For a quadratic $ax^{2}$ + bx + c, the sum of the roots is $-b/a$ . Here $a = -1$ and $b = 10$ , so the sum is -10/(-1) = 10. Alternatively, factoring - $x^{2}$ + $10x - 21$ = - $(x - 3) (x - 7)$ gives x-intercepts at $x = 3$ and $x = 7$ , and 3 + 7 = 10.

Why the others are wrong

AThis applies an incorrect sign when computing -b/a.
CThis uses the constant term instead of computing the sum of roots.
DThis incorrectly computes the sum using partial factorization or misidentified roots.

Question 4Easy

The function f is defined by $f(x) = (x - 2) (x + 6)$ . For what value of x does $f(x) = 0$ ?

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Why C is right

Setting $f(x) = 0$ gives $(x - 2) (x + 6) = 0$ . This equation is satisfied when $x - 2 = 0$ or $x + 6 = 0$ , so $x = 2$ or $x = -6$ . Of the choices given, -6 is a value for which $f(x) = 0$ .

Why the others are wrong

AThis incorrectly multiplies the values -2 and 6 instead of finding where each factor equals zero.
BThis incorrectly changes the sign of one of the x-intercepts.
DThis is the value that makes the first factor zero, resulting in x = 2, but then incorrectly applies a sign error.

Question 5Easy

The function f is defined by $f(x) = x^{2} + 6x + 9$ . What is the minimum value of f(x)?

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Why C is right

The expression $x^{2}$ + $6x + 9$ factors as $(x + 3)^{2}$ , which is a perfect square. Since $(x + 3)^{2} \ge 0$ for all real x, and equals 0 when $x = -3$ , the minimum value of f(x) is 0.

Why the others are wrong

AThis results from incorrectly using the constant term with a sign error as the minimum value.
BThis results from confusing the x-coordinate of the vertex with the minimum value of the function.
DThis results from incorrectly identifying the constant term as the minimum value without considering the function's behavior.

Question 6Easy

A scientist observes that a chemical compound has a mass of 640 grams and decreases to 80% of its mass every 3 days. Which function models the mass M in grams after d days?

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Why A is right

The mass decreases to 80% (multiplied by 0.8) every 3 days, so after d days there have been $d/3$ periods. Starting at 640 grams, the model is $M(d) = 640$ (0.8)^ $(d/3)$ .

Why the others are wrong

BThis interprets 'decreases to 80%' as 'decreases by 80%' (leaving 20%), confusing retention with reduction.
CThis applies the decay factor every day instead of every 3 days, missing the time-period adjustment.
DThis applies the exponent 3d instead of d/3, inverting the relationship between days and periods.

Question 7Easy

The function f is defined by $f(x) = x^{2} - 9$ . What is the product of the x-intercepts of the graph of $y = f$ (x) in the xy-plane?

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Why B is right

The x-intercepts occur when $f(x) = 0$ . Factoring $x^{2}$ - $9 = (x - 3) (x + 3) = 0$ gives $x = 3$ and $x = -3$ . The product of the x-intercepts is (3)(-3) = -9.

Why the others are wrong

AThis uses the constant term directly instead of computing the product of roots.
CThis incorrectly computes the sum of the roots (3 + (-3) = 0) instead of the product.
DThis incorrectly squares the constant term or computes 3² · 3² without considering signs.

Question 8Easy

The function f is defined by $f(x) = (x + 6) (x - 2)$ . For what value of x does $f(x) = 0$ ?

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Why A is right

The function $f(x) = 0$ when either factor equals zero. Setting $x + 6 = 0$ gives $x = -6$ , and setting $x - 2 = 0$ gives $x = 2$ . Since -6 is the only value among the choices, the answer is -6.

Why the others are wrong

BThis incorrectly uses the value from the second factor with a sign error.
CThis results from incorrectly computing the difference between the x-intercepts.
DThis results from incorrectly computing the product of the constants from the factors.

Question 9Easy

The function f is defined by $f(x) = 2(x + 3)^{2} - 8$ . What is the minimum value of f(x)?

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Why C is right

Since the function is in vertex form $f(x) = 2 (x + 3)^{2} - 8$ and the coefficient of the squared term is positive, the parabola opens upward. The minimum value occurs at the vertex, where $x = -3$ , giving f(-3) = $2(0)^{2} - 8 = -8$ .

Why the others are wrong

AThis choice confuses the x-coordinate of the vertex with the minimum value.
BThis choice results from computing f(0) = 2(3)² - 8 = 10 instead of finding the vertex value.
DThis choice results from dividing -8 by 2 instead of evaluating the function at the vertex.

Question 10Easy

A radioactive substance has an initial mass of 960 grams and decreases by 25% every 4 hours. Which function models the mass M in grams after h hours?

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Why A is right

A 25% decrease means the mass is multiplied by $1 - 0.25 = 0.75$ every 4 hours. After h hours, there have been $h/4$ periods, so $M(h) = 960$ (0.75)^ $(h/4)$ .

Why the others are wrong

BThis uses the reduction percentage (0.25) as the base instead of the retention factor (0.75).
CThis is a linear model treating the decay as constant subtraction rather than exponential decay.
DThis incorrectly uses 4h in the exponent instead of h/4, inverting the time-period relationship.

Question 11Easy

The function f is defined by $f(x) = x^{2} + 4x - 12$ . What is the y-intercept of the graph of $y = f$ (x) in the xy-plane?

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Why A is right

The y-intercept occurs when $x = 0$ . Substituting $x = 0$ into f(x) = $x^{2}$ + $4x - 12$ gives $f(0) = 0^{2} + 4$ (0) - 12 = -12. Therefore, the y-intercept is (0, -12).

Why the others are wrong

BThis incorrectly uses a positive value instead of the negative constant term.
CThis confuses the coefficient of the linear term with the y-intercept.
DThis incorrectly presents the constant term as an x-intercept rather than a y-intercept.

Question 12Easy

The function f is defined by $f(x) = x^{2} - 10x + 21$ . For what value of x does $f(x) = 0$ ?

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Why D is right

Setting $f(x) = 0$ gives $x^{2}$ - $10x + 21 = 0$ . Factoring yields $(x - 3) (x - 7) = 0$ , so $x = 3$ or $x = 7$ . Of the choices given, 7 is a value for which $f(x) = 0$ .

Why the others are wrong

AThis is the constant term in the function, not a value where f(x) = 0.
BThis incorrectly applies a sign error to one of the x-intercepts.
CThis is the coefficient of the linear term, not a value where f(x) = 0.

Question 13Easy

The function f is defined by f(x) = - $2(x - 5)^{2}$ . What is the maximum value of f(x)?

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Why C is right

Since the function is in vertex form $f(x) = -2 (x - 5)^{2}$ and the coefficient of the squared term is negative, the parabola opens downward. The maximum value occurs at the vertex, where $x = 5$ , giving f(5) = - $2(5 - 5)^{2} = 0$ .

Why the others are wrong

AThis choice results from evaluating f(0) = -2(0 - 5)² = -50 instead of finding the vertex.
BThis choice confuses the x-coordinate of the vertex with the maximum value.
DThis choice incorrectly assumes the parabola opens upward and uses an incorrect calculation.

Question 14Easy

A population of bacteria starts at 5,000 and increases by 15% each hour. Which function models the population P after t hours?

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Why B is right

A 15% increase means the population is multiplied by $1 + 0.15 = 1.15$ each hour. Starting at 5,000, the exponential model is $P(t) = 5$ ,000 $(1.15)^{t}$ .

Why the others are wrong

AThis represents a 15% decrease (multiplying by 0.85) rather than a 15% increase.
CThis is a linear model, not an exponential model; exponential growth requires the base raised to a power.
DThis uses 15 as the base instead of 1.15, dropping the hundredths place conversion from percentage.

Question 15Easy

The function f is defined by $f(x) = 2x^{2} - 8x + 6$ . What is the y-intercept of the graph of $y = f$ (x) in the xy-plane?

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Why C is right

The y-intercept occurs when $x = 0$ . Substituting $x = 0$ into $f(x) = 2x^{2} - 8x + 6$ gives f(0) = $2(0)^{2} - 8$ (0) + 6 = 6. Therefore, the y-intercept is (0, 6).

Why the others are wrong

AThis incorrectly uses the coefficient of the x-term as the y-coordinate of the y-intercept.
BThis incorrectly uses the leading coefficient as the y-coordinate of the y-intercept.
DThis reverses the coordinates, giving an x-intercept form instead of a y-intercept.

Question 16Easy

The function f is defined by $f(x) = (x - 1) (x + 5)$ . For what values of x does $f(x) = 0$ ?

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Why B is right

The function $f(x) = 0$ when $(x - 1) (x + 5) = 0$ . This occurs when either $x - 1 = 0$ or $x + 5 = 0$ , giving $x = 1$ or $x = -5$ .

Why the others are wrong

AThis reverses the signs of both x-intercepts.
CThis incorrectly treats both factors as having the same sign structure.
DThis reverses the sign of only the second x-intercept.

Question 17Easy

The function f is defined by $f(x) = (x + 5) (x - 4)$ . What is the minimum value of f(x)?

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Why A is right

The x-intercepts are at $x = -5$ and $x = 4$ , so the vertex x-coordinate is at their midpoint: (-5 + 4)/2 = -0.5. Substituting into f(x) gives f(-0.5) = (4.5)(-4.5) = -20.25. Since the parabola opens upward, this is the minimum.

Why the others are wrong

BThis results from calculating the product of the x-intercepts instead of evaluating the function at the vertex.
CThis results from incorrectly identifying the vertex as (1, -9) from averaging only the distances.
DThis results from taking the negative of the correct minimum value.

Question 18Easy

A town's population is 18,000 and increases by 6% each year. Which function models the population N after t years?

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Why A is right

A 6% increase means the population is multiplied by $1 + 0.06 = 1.06$ each year. Starting at 18,000, the exponential model is $N(t) = 18$ ,000 $(1.06)^{t}$ .

Why the others are wrong

BThis represents a 6% decrease (multiplying by 0.94) rather than a 6% increase.
CThis is a linear model computing 18,000 + 18,000(0.06)t = 18,000 + 1080t, not an exponential model.
DThis uses 6 as the base instead of 1.06, dropping the decimal conversion from percentage.

Question 19Easy

The function f is defined by $f(x) = x^{2} - 6x + 8$ . What is the y-intercept of the graph of $y = f$ (x) in the xy-plane?

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Why C is right

The y-intercept occurs when $x = 0$ . Substituting $x = 0$ into f(x) = $x^{2}$ - $6x + 8$ gives $f(0) = 0^{2} - 6$ (0) + 8 = 8. Therefore, the y-intercept is (0, 8).

Why the others are wrong

AThis incorrectly uses the coefficient of the x term as the y-coordinate.
BThis incorrectly identifies one of the x-intercepts (from factoring) as the y-intercept.
DThis reverses the coordinates, confusing the y-intercept with an x-intercept.

Question 20Easy

The function f is defined by $f(x) = -2 (x + 4) (x - 3)$ . What is the maximum value of f(x)?

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Why B is right

The x-coordinate of the vertex is the midpoint of the x-intercepts at $x = -4$ and $x = 3$ , which is $x = -0.5$ . Substituting -0.5 for x yields f(-0.5) = -2(-0.5 + 4)(-0.5 - 3) = -2(3.5)(-3.5) = 24.5.

Why the others are wrong

AThis results from giving the x-coordinate of the vertex instead of the maximum value.
CThis results from a sign error, not recognizing that the negative leading coefficient produces a maximum rather than a minimum.
DThis results from computing (x + 4)(x - 3) at the vertex without applying the coefficient -2.

What to do after easy

Getting these right quickly is the point: speed on the easy questions is what buys time for the hard ones. When they stop costing you effort, move up.

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Questions are written by SAT Climb and drawn from its own item bank. SAT® is a registered trademark of College Board, which is not affiliated with and does not endorse SAT Climb.

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