Transformations of Graphs

Front

What is the parent function of absolute value?

Back

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

Front

What is the parent function of quadratic functions?

Back

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

Front

What is the effect of translating a graph up by 5 units?

Back

Translating a graph up by 5 units means adding 5 to the function: f(x) becomes f(x) + 5.

Front

What is the effect of translating a graph left by 4 units?

Back

Translating a graph left by 4 units means replacing x with (x + 4): f(x) becomes f(x + 4).

Front

What is the equation of a quadratic function translated up 5 units?

Back

The equation is y = x² + 5.

Front

What is the equation of a quadratic function translated left 4 units and up 7 units?

Back

The equation is y = (x + 4)² + 7.

Front

What does a vertical stretch by a factor of 2 do to a function?

Back

A vertical stretch by a factor of 2 multiplies the function by 2: f(x) becomes 2f(x).

Front

What is the effect of reflecting a graph over the x-axis?

Back

Reflecting a graph over the x-axis changes the sign of the function: f(x) becomes -f(x).

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x.

Front

What is the parent function of cubic functions?

Back

The parent function of cubic functions is f(x) = x³.