Consider the function g(x) = 3x+2

Question

(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.