Question

AJ graphs the function f(x) = -(x +2)^2 - 1 picture shown below.

Part 1: What mistake did AJ make in the graph?

Part 2: Evaluate any two x-values (between -5 and 5) into AJ's function. Show your work. How does your work prove that AJ made a mistake in the graph?

Answer 1

Part 1: AJ reflected the graph over x-axis.

Part 2: The two x-values are
`(0,-5)` and
`(-1,-2)` . AJ plotted the graph using the function
`f(x)=(x+2)^(2)-1` . This resulted the graph to reflect over x-axis.

Explanation:

Part 1: AJ mistakenly plotted over x-axis, which means he reflected the graph over x-axis.The x-value remains the same. Only the y-values are transformed into its opposite sign.

Part 2:

Step 1: Plotting any two values for the function
`f(x)=-(x+2)^(2)-1`

Substituting x=0, we get,

`\begin{aligned}y &=f(0)=-(0+2)^(2)-1 \\&=-(2)^(2)-1 \\&=-4-1=-5 \\y &=-5\end{aligned}`

Substituting x=-1, we get,

`\begin{aligned}y &=f(-1)=-(-1+2)^(2)-1 \\&=-(1)^(2)-1 \\&=-1-1=-2 \\y &=-2\end{aligned}`

The two x-values for AJ’s function is
`(0,-5)` and
`(-1,-2)`

Step 2:

AJ plotted the graph using the function
`f(x)=(x+2)^(2)-1` . This resulted the graph to reflect over x-axis.