Question

Abe, Mary, and Stephen were asked to graph thefunction y = –2 + log, (x + 1).Who is correct and why? Justify your reasoning.AbeMaryStephen

Answer 1

Given the function:

$y=-2+\log _2(x+1)$

To compare the graphs, follow the steps below.

Step 1: Choose a value for x in order to evaluate the graphs.

Let's choose x = 0.

Then, substituting x by 0 in the equation:

$\begin{gathered} y=-2+\log _2(0+1) \\ y=-2+\log _2(1) \end{gathered}$

Step 2: Solve the equation above.

Knowing that log₂(1) is 0:

$\begin{gathered} y=-2+0 \\ y=-2 \end{gathered}$

So, the graph must have the point (0, -2).

Step 3: Find the point (0, -2) in the graphs.

Comparing the graphs, we can observe that only the graph drawn by Stephen contains the point (0, -2).

Answer: Stephen.