Transformations of Functions and Graphs

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

Front

What does it mean to shift a graph vertically?

Back

Shifting a graph vertically means moving it up or down on the coordinate plane without changing its shape.

Front

What is the effect of adding a constant to a function, f(x) + k?

Back

Adding a constant k to a function f(x) shifts the graph vertically by k units. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the effect of subtracting a constant from the input of a function, f(x - k)?

Back

Subtracting a constant k from the input of a function shifts the graph horizontally to the right by k units.

Front

What is the effect of multiplying a function by a constant, kf(x)?

Back

Multiplying a function by a constant k vertically stretches the graph if k > 1, compresses it if 0 < k < 1, and reflects it across the x-axis if k is negative.

Front

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

Back

The range of the function f(x) = x^2 is [0, ∞) because the output values are always non-negative.

Front

How do you identify a vertical stretch in a function?

Back

A vertical stretch occurs when the function is multiplied by a factor greater than 1, such as g(x) = 2f(x), which makes the graph taller.

Front

What is the equation of an absolute value function shifted right by 5 units?

Back

The equation of an absolute value function shifted right by 5 units is y = |x - 5|.

Front

What is the effect of a negative sign in front of a function, -f(x)?

Back

A negative sign in front of a function reflects the graph across the x-axis.

Front

What does the notation f(x) + k represent?

Back

The notation f(x) + k represents a vertical shift of the graph of f(x) by k units.