2. 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 D: Use the original function and find the x-value for whichf(x)=−1

x=


Part E: Use the original function and find f(0)
.

f(0) =

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

f(0)
is the

Answer 1

Let's go through each part step by step.

Part A:

• For graphing the function \( f(x) = 5x - 6 \), you would graph it on Desmos using the provided link. This line has a slope of 5 and a y-intercept of -6.

Part B:

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

Part C:

To solve \( -1 = 5x - 6 \): \[ -1 + 6 = 5x \] \[ 5 = 5x \] \[ x = 1 \]

Part D:

To find the x-value for which \( f(x) = -1 \): \[ 5x - 6 = -1 \] Adding 6 to both sides: \[ 5x = 5 \] Dividing both sides by 5: \[ x = 1 \]

Part E:

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

Part F:

The key feature shown by \( f(0) \) is the y-intercept because it represents the value of the function when \( x = 0 \). Hence, you can say:

\( f(0) \) is the y-intercept (specifically, \( -6 \)).

If you need any further assistance with this function or related concepts, feel free to ask!