Transformations of Graphs

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x².

Front

What is the parent function of an absolute value equation?

Back

The parent function of an absolute value equation is f(x) = |x|.

Front

What effect does multiplying a quadratic function by a factor greater than 1 have on its graph?

Back

It makes the graph steeper.

Front

What is a vertical shift in the context of graph transformations?

Back

A vertical shift moves the graph up or down without changing its shape.

Front

What is a horizontal shift in the context of graph transformations?

Back

A horizontal shift moves the graph left or right without changing its shape.

Front

How does the equation g(x) = 2x² differ from f(x) = x²?

Back

g(x) = 2x² is a vertical stretch of the parent function f(x) = x².

Front

Which transformation does the equation g(x) = x² + 3 represent?

Back

A vertical shift upward by 3 units.

Front

What does the equation g(x) = x² - 4 represent?

Back

A vertical shift downward by 4 units.

Front

How do you determine if a function is steeper than another?

Back

Compare the coefficients of x in linear functions; a larger coefficient indicates a steeper line.

Front

Order the following functions from steepest to least steep: y = 5x, y = 1/2x, y = 3x, y = 1/3x.

Back

Steepest to least steep: y = 5x, y = 3x, y = 1/2x, y = 1/3x.