Task Sets: Read inverse from graph or table - Common Core Math - HS Functions

Concepts

Use the table below to answer the question.

What is $f^{-1}(7)$ ?

Enter a number.

The graph of $f$ passes through the points $(1, 3)$ , $(2, 5)$ , $(3, 7)$ , and $(4, 9)$ .

Using the horizontal-line method, what is $f^{-1}(5)$ ?

Cannot be determined without the formula

The graph of $f$ contains the point $(3, 7)$ .

If you reflect this point over the line $y = x$ to construct the graph of
$f^{-1}$ , which point is on the graph of $f^{-1}$ ?

$(7, 3)$

$(3, -7)$

$(-3, 7)$

$(3, 7)$

Use the table below.

What is $f^{-1}(14)$ ?

The graph of $f$ passes through these points:
$(0, 2)$ , $(1, 5)$ , $(2, 8)$ , $(3, 11)$ .

Using the horizontal-line method, what is $f^{-1}(8)$ ?

The table for $f$ is shown below.

You construct the inverse table by swapping the columns.
In the inverse table, what is the output ( $f^{-1}(x)$ ) when the input is 9?

A student is given the following table.

Can an inverse function $f^{-1}$ be built from this table?

Yes — every row has a different x-value, so the inverse exists.

No — the output value 5 appears twice, so the function is not one-to-one.

Yes — the table has four rows, which is enough for an inverse.

No — only tables with consecutive integers can have inverses.