Chapter 4.3, Problem 2STP

For Exercises $1-5,$ choose the correct letter.

The following ordered pairs represent a function: (-2,10),(-1,7),(0,6),(1,7) and (2, 10). Which equation could represent the function?

F. $y=-4x+2$

G. $y=x^2-6$

H. $y=5x$

I. $y=x^2+6$

To determine

To select the correct function that could be represent for the given ordered pairs.

Answer to Problem 2STP

  $\text{I}\text{. }y=x^2+6$

Explanation of Solution

Given information: Ordered pairs $\left(-2,10\right),\left(-1,7\right),\left(0,6\right),\left(1,7\right)\text{ and }\left(2,10\right)$ .

Formula used: Slope of line $\left(m\right)=\frac{y_2-y_1}{x_2-x_1}$ where $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are any two points from given table.

Slope- intercept form of line: $y=mx+b$ . Where m is slope and b is y- intercept.

Calculation: First let us check the differences of x and y -coordinate values The differences of x -coordinate values of ordered pairs is 1 but the differences of y -coordinate values is not a constant.

  $\begin{array}{l}7-10=-3\hfill \\ 6-7=-1\hfill \\ 7-6=1\hfill \\ 10-7=3\hfill \end{array}$

So, given ordered pairs could not represent a linear function.

Now, check by plugging x -coordinate values in options $G.y=x^2-6$ and $\text{I}\text{. }y=x^2+6$ , function $y=x^2+6$ gives y -coordinate values {10,7,6,7,10} on plugging x -coordinate values {-2,-1, 0,1,2}.

Therefore, for $y=x^2+6$ is the correct function that is represented by given ordered pairs $\left(-2,10\right),\left(-1,7\right),\left(0,6\right),\left(1,7\right)\text{ and }\left(2,10\right)$ .