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 transformation occurs when f(x) is replaced with f(x) + k?

Back

A vertical translation of the graph by k units. If k is positive, the graph moves up; if k is negative, it moves down.

Front

What transformation occurs when f(x) is replaced with f(x - h)?

Back

A horizontal translation of the graph by h units. If h is positive, the graph moves right; if h is negative, it moves left.

Front

What is the effect of multiplying f(x) by -1?

Back

It reflects the graph of the function across the x-axis.

Front

What is the effect of multiplying f(x) by a value greater than 1?

Back

It vertically stretches the graph, making it steeper.

Front

What is the effect of multiplying f(x) by a value between 0 and 1?

Back

It vertically compresses the graph, making it less steep.

Front

What type of function is f(x) = |x|?

Back

Absolute value function.

Front

What type of function is f(x) = x^2?

Back

Quadratic function.

Front

What type of function is f(x) = √x?

Back

Square root function.

Front

What is the general form of a linear function?

Back

f(x) = mx + b, where m is the slope and b is the y-intercept.