Question

consider the graph shown below. answer the two test questions that relate to the graph. absolute value functions
22 how is the graph of the function related to the parent absolute value function? select all that apply.
a the vertex was shifted 1 to the right.
b the vertex was shifted 4 up.
c the vertex was shifted 1 to the left.
d the graph is vertically compressed by 1/2
e the graph is vertically stretched by 2
f the vertex was shifted 4 down.

Explanation:

Step1: Identify parent function

Parent absolute value function: $y = |x|$ (vertex at (0,0)).

Step2: Analyze vertex shift

Graph vertex is at (-1,0). Shift left 1: $y = |x + 1|$.

Step3: Analyze vertical stretch

Slope of parent is 1; graph slope is 2. Stretch by 2: $y = 2|x + 1|$.

Step4: Match options

Vertex shifted left 1 (B), vertically stretched by 2 (E).

Answer:

B. The vertex was shifted 1 to the left, E. The graph is vertically stretched by 2