Question

Use the graph to answer the question.Which of the following functions is represented by the graph?A. identity y=xB. reciprocal y=1/xC. constant y=cD. exponential y=b^x

Answer 1

We are given a graph and we are asked to determine the type of function.

We notice that the graph is a line, therefore, it must be of the form:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

The y-intercept "b" is the point where the line crosses the y-axis since from the graph we notice that the line crosses the y-axis at y = 0, we have:

`\begin{gathered} y=mx+0 \\ y=mx \end{gathered}`

Also, we notice that the point:

`(x,y)=(1,1)`

Is part of the line, therefore, we can substitute in the equation and we get:

`\begin{gathered} 1=m(1) \\ 1=m \end{gathered}`

Therefore, the slope is 1. Substituting we get:

`y=x`

Therefore, the right answer is identity y = x.