Function Transformation

Front

What is a vertical shift in function transformation?

Back

A vertical shift occurs when a function is moved up or down on the graph. For example, f(x) + k shifts the graph up by k units if k > 0 and down by k units if k < 0.

Front

What does the transformation k(x) = f(x) - 9 represent?

Back

The transformation represents a vertical shift down by 9 units.

Front

What is a horizontal shift in function transformation?

Back

A horizontal shift occurs when a function is moved left or right on the graph. For example, f(x + k) shifts the graph left by k units if k > 0 and right by k units if k < 0.

Front

What does the transformation m(x) = f(x + 1) represent?

Back

The transformation represents a horizontal shift left by 1 unit.

Front

What is a vertical stretch in function transformation?

Back

A vertical stretch occurs when the output of a function is multiplied by a factor greater than 1, making the graph taller. For example, g(x) = af(x) where a > 1.

Front

What does the transformation g(x) = 2f(x) represent?

Back

The transformation represents a vertical stretch by a factor of 2.

Front

What is a vertical compression in function transformation?

Back

A vertical compression occurs when the output of a function is multiplied by a factor between 0 and 1, making the graph shorter. For example, g(x) = af(x) where 0 < a < 1.

Front

What type of function is represented by the equation y = |x|?

Back

The function is an absolute value function.

Front

What does the transformation y = (x - 2)^3 + 4 represent?

Back

The transformation represents a horizontal shift right by 2 units and a vertical shift up by 4 units.

Front

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

Back

The negative sign reflects the graph of the function across the x-axis.