Consider the function f(x) = 5x−6

Question

(1 point)
Part A: Graph the function using Desmos. (Link to Desmos).

Part B: Find f(7)

f(7) =

Part C: Solve −1 = 5x−6
.

x=


Part C: Find the x-value for whichf(x)=−1

x=


Part D: Find f(0)
.

f(0) =

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

f(0)
is the

Answer 1

Sure! Let's go through each part step by step.

Part A: Graph the function

To graph the function \( f(x) = 5x - 6 \) using Desmos, you can simply enter the equation in the Desmos graphing calculator online. However, I cannot display an actual graph here, but you can easily visualize it as a straight line due to it being a linear function.

Part B: Find \( f(7) \)

To find \( f(7) \): \[ f(7) = 5(7) - 6 \] \[ f(7) = 35 - 6 = 29 \] So, \( f(7) = 29 \).

Part C: Solve \( -1 = 5x - 6 \)

To solve the equation \( -1 = 5x - 6 \):

1. Add 6 to both sides: \[ -1 + 6 = 5x \] \[ 5 = 5x \]

2. Divide by 5: \[ x = 1 \]

Part D: Find \( f(0) \)

To find \( f(0) \): \[ f(0) = 5(0) - 6 \] \[ f(0) = 0 - 6 = -6 \] So, \( f(0) = -6 \).

Part E: What is a key feature of \( f(0) \)?

In this case, \( f(0) = -6 \) means that the y-intercept of the graph is \(-6\). So, specifically, we can say:

• The y-intercept of \( f(x) = 5x - 6 \) is \(-6\).

To summarize:

• Part B: \( f(7) = 29 \)
• Part C: \( x = 1 \)
• Part D: \( f(0) = -6 \)
• Part E: \( f(0) \) is the y-intercept.