Question

for exercises 75–84, determine the x- and y-intercepts for the given function. (see example 7)

1. $f(x) = 2x - 4$
2. $g(x) = 3x - 12$
3. $h(x) = |x| - 8$
4. $k(x) = -|x| + 2$
5. $p(x) = -x^2 + 12$
6. $q(x) = x^2 - 8$
7. $r(x) = |x - 8|$
8. $s(x) = |x + 3|$
9. $f(x) = \sqrt{x} - 2$
10. $g(x) = -\sqrt{x} + 3$

Explanation:

Let's solve problem 75: \( f(x) = 2x - 4 \)

Step 1: Find the x-intercept

To find the x-intercept, set \( f(x) = 0 \) (since the x-intercept is where \( y = 0 \)).
So, \( 0 = 2x - 4 \)
Add 4 to both sides: \( 2x = 4 \)
Divide both sides by 2: \( x = 2 \)
So the x-intercept is \( (2, 0) \).

Step 2: Find the y-intercept

To find the y-intercept, set \( x = 0 \) (since the y-intercept is where \( x = 0 \)).
Substitute \( x = 0 \) into \( f(x) \): \( f(0) = 2(0) - 4 = -4 \)
So the y-intercept is \( (0, -4) \).

Answer:

x-intercept: \( (2, 0) \), y-intercept: \( (0, -4) \)