# Lesson 11

Zeros of Functions and Intercepts of Graphs

• Let’s see what happens when a function’s input or output is 0.

### 11.1: Which Output is 0?

Which of these functions have an output of 0 when the input is -4?

• $$v(x)=4x$$
• $$w(x)=\text-4x$$
• $$y(x)=8+2x$$
• $$z(x)=2x-8$$

### 11.2: Intercept Detective

Here are the definitions of some functions, followed by some possible inputs for the functions.

$$a(x)=x - 5$$

$$b(x)=x + 5$$

$$c(x)=x-3$$

$$d(x)=x+1$$

$$f(x)=3x - 6$$

$$g(x)=3x + 6$$

$$h(x)=(x+5)(x+3)$$

$$m(x)=(x+1)(x-3)$$

$$n(x)=(3x-6)(x-5)$$

Possible inputs: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, and 5.

1. For each function, decide which input or inputs would give an output of 0.
2. Here are graphs of $$b$$, $$f$$, and $$m$$. Label each intercept with its coordinates, and be prepared to explain how you know.

### 11.3: Making More Connections

1. For each function, identify the input that would give an output of 0.
• $$p(x) = x + 10$$
• $$q(x) = x - 10$$
• $$r(x) = 8 - x$$
• $$s(x) = \text-8 - x$$
• $$t(x) = 2x - 8$$
• $$u(x) = 2x + 8$$
• $$v(x) = (x + 10)(2x - 8)$$
• $$w(x) = (2x + 8)(10 - x)$$