Transformations of Functions

Front

What is the domain of an exponential function?

Back

All Real Numbers

Front

What is the range of the graph of an exponential function?

Back

y ≥ -1

Front

What is the range of the exponential function y = a^x where a > 0?

Back

y > 0

Front

If the vertex of the quadratic function f(x) is (-4, 5) and g(x) = f(x + 2), what is the vertex of g(x)?

Back

(-6, 5)

Front

Identify the y-intercept of the function f(x) = 2x - 3.

Back

(0, -3)

Front

What transformation occurs when a function is shifted to the right by 3 units?

Back

The new function is f(x - 3).

Front

What is a vertical stretch of a function?

Back

Multiplying the function by a factor greater than 1.

Front

What is a vertical compression of a function?

Back

Multiplying the function by a factor between 0 and 1.

Front

What does it mean for a function to be reflected over the x-axis?

Back

The function is multiplied by -1.

Front

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

Back

It shifts the graph vertically.