Questions: Graph the following piecewise function. f(x) = - -3 if x ≤ 1 - -1 if x > 1 Choose the correct graph below. A. [Graph option A] B. [Graph option B] C. [Graph option C] D. [Graph option D]

Graph the following piecewise function.

f(x) =
- -3 if x ≤ 1
- -1 if x > 1

Choose the correct graph below.

A. [Graph option A]
B. [Graph option B]
C. [Graph option C]
D. [Graph option D]

Transcript text: Graph the following piecewise function. f(x) = \begin{cases} -3 & \text{if } x \leq 1 \\ -1 & \text{if } x > 1 \end{cases} Choose the correct graph below. A. [Graph option A] B. [Graph option B] C. [Graph option C] D. [Graph option D] This test: 30 point(s) possible This question: 1 point(s) possible Question 6 of 30 Submit test Time Remaining: 02:55:36 Next

Solution

Solution Steps

Step 1: Understand the Piecewise Function

The given piecewise function is: \[ f(x) = \begin{cases} 3x + 1 & \text{if } x \leq 1 \\ x - 1 & \text{if } x > 1 \end{cases} \]

Step 2: Graph the First Piece

For \( x \leq 1 \), the function is \( f(x) = 3x + 1 \). This is a linear function with a slope of 3 and a y-intercept of 1. We need to plot this line for all \( x \) values less than or equal to 1.

Step 3: Graph the Second Piece

For \( x > 1 \), the function is \( f(x) = x - 1 \). This is a linear function with a slope of 1 and a y-intercept of -1. We need to plot this line for all \( x \) values greater than 1.

Step 4: Combine the Graphs

Combine the two pieces on the same graph. Ensure that the first piece ends at \( x = 1 \) and the second piece starts just after \( x = 1 \).

Step 5: Choose the Correct Graph

Compare the combined graph with the given options to select the correct one.