Find the x and y intercepts of f(x) and g(x) when f(x)=3x+8 and g(x)=1/2f(x)

Answer 1

Hi Chris,

This is a great question! Looking at both of these functions, we know that we will need to solve for g(x). The function f(x) is in the function g(x). Therefore, we will plug this into the original equation. See below:

g(x)= 1/2(3x+8)

After distributing the 1/2, we get the following equation: g(x)= 3/2x + 4

Now, we will solve for the x and y intercepts!

Let's start with f(x).

To find the y intercept, we will plug in 0 for x.

1. y = 3(0) + 8
2. y = 8
3. y intercept is (0,8)

To find the x intercept, we will now plug in 0 for y.

1. 0 = 3x + 8
2. -8 = 3x
3. x = -8/3
4. x intercept is (-8/3,0)

Now we will do the same for g(x), which we solved for.

1. x intercept means we plug in 0 for y.
2. 0 = 3/2x + 4
3. -4 = 3/2x
4. x = -8/3
5. x intercept is (-8/3,0)

To find the y we will plug in 0 for x again.

1. y = 3/2(0) + 4
2. y = 4
3. y intercept is (0,4)

You have four solutions total! (-8/3,0), (0,8), (-8/3,0), (0,4) Hope this helps!