M3 Mid Exam Function Transformations Compositions Inverses

Front

What is the transformation of the function p(x) = f(x + 3)?

Back

Left 3 units.

Front

If f(x) = 2x and g(x) = 2x^2 - 1, what is f(g(3))?

Back

34.

Front

If f(x) = \frac{1}{x} and g(x) = 3x + 2, what is f(g(x))?

Back

\frac{1}{3x + 2}.

Front

If f(x) = 2x and g(x) = 2x^2 - 1, what is g(f(-1))?

Back

7.

Front

Is the function g(x) = \sqrt{-x - 8} reflected over the x-axis or the y-axis?

Back

y-axis.

Front

What does a transformation of 'Right 3 units' mean for the function f(x)?

Back

The function is shifted 3 units to the right on the graph.

Front

What is the composition of functions f(g(x))?

Back

It means to apply g(x) first, then apply f to the result.

Front

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

Back

f^{-1}(x) = \frac{x}{2}.

Front

How do you find the inverse of a function algebraically?

Back

Replace f(x) with y, swap x and y, and solve for y.

Front

What is the effect of a vertical stretch on a function?

Back

It multiplies the output values of the function by a factor greater than 1.