Function Families

Front

What is a function family?

Back

A group of functions that share common characteristics and can be represented by similar equations.

Front

What is a transformation in the context of functions?

Back

A change made to a function that alters its graph, such as shifting, reflecting, stretching, or compressing.

Front

What does a horizontal shift to the right by 'h' units mean for the function f(x)?

Back

The new function is f(x-h), moving the graph to the right.

Front

What does a vertical shift up by 'k' units mean for the function f(x)?

Back

The new function is f(x) + k, moving the graph up.

Front

What is the parent function of a quadratic function?

Back

The parent function is f(x) = x².

Front

What is the parent function of an absolute value function?

Back

The parent function is f(x) = |x|.

Front

What is the parent function of an exponential function?

Back

The parent function is f(x) = a^x, where a > 0.

Front

What is the effect of a negative sign in front of a function?

Back

It reflects the graph across the x-axis.

Front

What is the effect of a coefficient greater than 1 in front of a function?

Back

It vertically stretches the graph.

Front

What is the effect of a coefficient between 0 and 1 in front of a function?

Back

It vertically compresses the graph.