What this lesson covers
- The one switch that decides every intercept question
- Why the point (4, 0) and the point (0, 4) are not the same answer
- "A zero of f" and "the x-intercept" mean the same thing, and f(0) does not
- The same switch on a factored form
- A practice problem going the other direction
Chapters
- 0:00Both are real. One was asked.
- 0:04Four choices, two numbers
- 0:17The setup: f(x) = 3x - 12
- 0:38One switch, both directions
- 1:31A zero of f is not f(0)
- 2:09Your turn
- 2:47Three ways this goes wrong
- 3:07x-intercept, y is zero
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:17The setup: f(x) = 3x - 12
The function f of x equals three x minus twelve. The question asks for the x intercept of its graph. Four choices, and every one of them is some arrangement of a four and a negative twelve. This is not a solving problem. It is a which zero problem.
0:38One switch, both directions
One switch decides everything. An x intercept is where the graph crosses the x axis, and on that axis, y is zero. So set f of x to zero. Zero equals three x minus twelve. Solve it. Add twelve. Divide by three. x equals four. The point is four comma zero. The x you solved for rides in the first slot, and the zero you planted rides in the second. Now flip the switch the other way. The y intercept sets x to zero. f of zero is three times zero minus twelve. Negative twelve. The point is zero comma negative twelve. Choice A is a real intercept. It is just not the one they asked for.
1:31A zero of f is not f(0)
Three phrases, and two of them are the same thing. A zero of f, and the x intercept, both mean solve f of x equals zero. But f of zero is the other switch position. It is the y intercept. The vocabulary is the trap. One more form. f of x equals two times, open paren, x minus six. Set it to zero, and the paren does the work. x equals six. But f of zero is two times negative six. Negative twelve. Same switch, either direction, any form.
2:09Your turn
g of x equals negative two x plus ten. What is the y intercept of the graph of g? y intercept. So the switch goes to x equals zero. g of zero is negative two times zero, plus ten. Ten. The point is zero comma ten. Not five comma zero, that is the other crossing. The answer is C.
2:47Three ways this goes wrong
Three ways this goes wrong. Solving the right equation and reporting the wrong point, four comma zero is not zero comma four. Answering the other intercept entirely. And hearing f of zero when the question said zero of f. Flip the phrase, flip the switch.
3:07x-intercept, y is zero
x intercept, y is zero. y intercept, x is zero. One switch.
Read the written version: the Linear functions strategy guide, then try 25 hard Linear functions questions with full explanations. Both are free, no account needed.