2.7 Parent Functions and Transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which retains the essential characteristics of that family.

Front

What is the parent function for a quadratic function?

Back

f(x) = x²

Front

What is the parent function for an absolute value function?

Back

f(x) = |x|

Front

Describe the transformation: f(x) = (x - 3)².

Back

Shifts right 3 units.

Front

Describe the transformation: f(x) = |x| + 2.

Back

Shifts up 2 units.

Front

Which equation represents a quadratic function translated left 4 units?

Back

y = (x + 4)²

Front

Describe the transformation: f(x) = |x + 5|.

Back

Shifts left 5 units.

Front

What does it mean to translate a function?

Back

To translate a function means to shift it horizontally or vertically without changing its shape.

Front

Describe the transformation: f(x) = x² - 3.

Back

Shifts down 3 units.

Front

What is the effect of a negative sign in front of a function, e.g., f(x) = -|x|?

Back

It reflects the function across the x-axis.