Review of Parent Functions and Transformations

Front

What is the equation of the PARENT function?

Back

f(x) = x^3

Front

Which transformation maps the graph of f(x) = x^2 to g(x) = (x + 4)^2?

Back

A translation shifting f(x) 4 units to the left.

Front

What is f(-1) if f(x) = x^2 - 1?

Back

-2

Front

Which equation transforms f(x) = x to a vertical stretch by a factor of 2, a reflection over the x-axis, and a shift down 4?

Back

-f(2x) - 4

Front

What type of function is shown: f(x) = √x?

Back

Square root function.

Front

What is the general form of a quadratic function?

Back

f(x) = ax^2 + bx + c, where a ≠ 0.

Front

What does a vertical stretch by a factor of k do to the graph of f(x)?

Back

It multiplies the output of f(x) by k, making the graph taller.

Front

What is the effect of a horizontal shift to the right on the function f(x)?

Back

The function becomes f(x - h) for a shift of h units to the right.

Front

What is the parent function of a cubic function?

Back

f(x) = x^3.

Front

What transformation is represented by g(x) = f(x) + k?

Back

A vertical shift of k units up if k > 0, down if k < 0.