Question

Sketch the graph or the inverse of the function pictured

Answer 1

Step 1:

Draw the table for the input x and output y.

Step 2:

From the table, we can see that the function is an exponential function.

$\begin{gathered} y=x^2 \\ \text{for x = 0, y = 0} \\ \text{for x = 1, y = 1} \\ \text{for x = 2, y = 4} \\ \text{for x = 3, y = 9} \\ \text{Hence, y = x}^2 \end{gathered}$

Step 2:

Find the inverse of the function.

$\begin{gathered} y=x^2 \\ \text{The inverse of } \\ y=x^2 \\ is \\ y\text{ = }\pm\sqrt[]{x} \end{gathered}$

Step 3:

The two graphs below, show the graph of the inverse for both negative and positive square roots of x.

$\text{The blue graph above shows the graph for y = +}\sqrt[]{x}$

$\text{The blue graph above shows the graph of y = -}\sqrt[]{x}$

Final answer

The blue graph is the inverse of the red graph.