Question

Consider the function g(x) = 3x+2
(4 points)
Part A: Graph the function using Desmos. (Link to Desmos).

Part B: Find g(8)

g(8) = ____

Part C: Solve −1 = 3x+2.

x=____


Part D: Use the original function and find the x-value for whichg(x)=8

x=____


Part E: What is the key feature shown by g(0)
? (Write slope, x-intercept, y-intercept, vertex, axis of symmetry, minimum, maximum)

g(0) is the ___

Answer 1

Let's tackle each part of your question step-by-step.

### Part A: Graph the function
For Part A, you can use the function \( g(x) = 3x + 2 \) and enter it into Desmos to graph it. Unfortunately, I cannot create or display graphs here, but you can easily plot it on the Desmos graphing calculator.

### Part B: Find \( g(8) \)
To find \( g(8) \):
\[
g(8) = 3(8) + 2 = 24 + 2 = 26
\]
Thus, \( g(8) = 26 \).

### Part C: Solve \( -1 = 3x + 2 \)
To solve for \( x \):
1. Start with the equation:
\[
-1 = 3x + 2
\]
2. Subtract 2 from both sides:
\[
-1 - 2 = 3x
\]
\[
-3 = 3x
\]
3. Divide by 3:
\[
x = -1
\]
Thus, \( x = -1 \).

### Part D: Find the x-value for which \( g(x) = 8 \)
We need to solve the equation \( g(x) = 8 \):
1. Set the equation:
\[
3x + 2 = 8
\]
2. Subtract 2 from both sides:
\[
3x = 6
\]
3. Divide by 3:
\[
x = 2
\]
Thus, \( x = 2 \).

### Part E: Key feature shown by \( g(0) \)
To find \( g(0) \):
\[
g(0) = 3(0) + 2 = 2
\]
Thus, \( g(0) = 2 \), and in terms of key features:
- \( g(0) \) gives the **y-intercept** of the function, because it represents the value of the function when \( x = 0 \).

In summary:
- **Part B:** \( g(8) = 26 \)
- **Part C:** \( x = -1 \)
- **Part D:** \( x = 2 \)
- **Part E:** \( g(0) \) is the **y-intercept**.