Question

practice & problem solving
classify each function as even, odd, or neither.
36.
37.

1. error analysis a student says the graph of

f(x) = 0.5x⁴ + 1 is a vertical stretch and a
translation up 1 unit of the parent function.
explain the student’s error. mp.3

Explanation:

Problem 36:

Step1: Recall symmetry rules

A function is even if its graph is symmetric about the \( y \)-axis, odd if symmetric about the origin.

Step2: Analyze Graph 36

The graph (36) is symmetric across the \( y \)-axis (left and right of \( y \)-axis mirror).

Step1: Recall symmetry rules

Check symmetry about \( y \)-axis (even) or origin (odd).

Step2: Analyze Graph 37

The graph (37) is not symmetric about \( y \)-axis (left/right differ) nor origin (no rotational symmetry).

Step1: Recall transformation rules

For \( y = a f(x)+k \), \( |a| > 1 \) is stretch, \( 0 < |a| < 1 \) is compression.

Step2: Analyze \( f(x)=0.5x^4 + 1 \)

Here, \( a = 0.5 \) ( \( 0 < 0.5 < 1 \) ), so it’s a vertical compression (not stretch) and translation up 1.

Answer:

Even

Problem 37: