Consider the relationship between y = f(x) and y = f (-х).

Question

Question 1: What is this type of function transformation called? What does it look like on a graph?

Question 2: The parent function is f(x) = x^2. On a sheet of graph
paper, sketch both y = f(x) and y = f (-x) for the parent
function. Be sure to clearly label each sketch.

Answer each question, 1 sentence each.

Answer 1

Question 1: The transformation from \( y = f(x) \) to \( y = f(-x) \) is called a reflection across the y-axis, and on a graph, it appears as a mirror image of the original function on the left side of the y-axis.

Question 2: For the parent function \( f(x) = x^2 \), the sketch of \( y = f(x) \) is a parabola opening upwards with its vertex at the origin (0,0), and the sketch of \( y = f(-x) \) is identical since \( x^2 \) is an even function, both providing the same parabola shape.