Question

Use the following functions to answer each question:

f(x)= 2x - 3 g(x)= -4x -1

What is f(3)?

Which function has a steeper slope?




Use the following functions to answer each question:

f(x) = 2x -3 4x - 7y = 28

Which function has the greater y-intercept?


What is f(-2)?

Answer 1

Let's analyze the functions step by step.

### First set of functions:
1. **Calculating \( f(3) \)**:
\[
f(x) = 2x - 3
\]
Thus,
\[
f(3) = 2(3) - 3 = 6 - 3 = 3
\]

2. **Determining which function has a steeper slope**:
- The slope of \( f(x) = 2x - 3 \) is **2**.
- The slope of \( g(x) = -4x - 1 \) is **-4** (considered in absolute value, it's 4).
Since the absolute value of -4 is greater than 2, function \( g(x) \) has a steeper slope.

### Summary of the first set:
- \( f(3) = 3 \)
- The function with the steeper slope is \( g(x) \).

---

### Second set of functions:
1. **Finding the y-intercept of each function**:
- For \( f(x) = 2x - 3 \): The y-intercept is when \( x = 0 \):
\[
f(0) = 2(0) - 3 = -3
\]

- For the equation \( 4x - 7y = 28 \), we need to solve for \( y \):
\[
4x - 7y = 28 \implies -7y = -4x + 28 \implies y = \frac{4}{7}x - 4
\]
The y-intercept here is when \( x = 0 \):
\[
y(0) = \frac{4}{7}(0) - 4 = -4
\]

Now we can compare the y-intercepts:
- The y-intercept of \( f(x) \) is **-3**.
- The y-intercept from \( 4x - 7y = 28 \) is **-4**.

Thus, **\( f(x) \)** has a greater y-intercept.

2. **Calculating \( f(-2) \)**:
\[
f(x) = 2x - 3
\]
Therefore,
\[
f(-2) = 2(-2) - 3 = -4 - 3 = -7
\]

### Summary of the second set:
- The function with the greater y-intercept is \( f(x) \).
- \( f(-2) = -7 \).