Question

Which parent function is represented by the table?A. f(x)= x^2B. f(x)= 2^xC. f(x)= lxlD. f(x)= x

Answer 1

The parent function can be determined by direct substitution of the x values in the table into the expressions of each function. Otherwise, we could also just plot the points given in the table on a graph and observe the form of the graph, and this will help us choose the right option.

By Substitution method:

a) Given that f(x) = x^2

$\begin{gathered} \text{ when x =-}2 \\ f(x)=(-2)^2=4 \end{gathered}$

This tallies with the y value in the table.

Again:

$\begin{gathered} \text{ when x = -1} \\ f(x)=(-1)^2=1 \end{gathered}$

Since the y values tally with that given in the table, we can conclude that the parent function is f(x) = x^2

b) Given that f(x) = 2^x

$\begin{gathered} \text{ when x = -2} \\ f(x)=2^{(-2)}=\frac{1}{4} \end{gathered}$

This does not tally with the y value in the table

c) Given that f(x) = |x|

$\begin{gathered} \text{when x = -2} \\ f(x)=\lvert-2\rvert=2 \end{gathered}$

This does not tally with the y value in the table

d) Given that f(x) = x

$\begin{gathered} \text{when x = -2} \\ f(x)=-2 \end{gathered}$

This also does not tally with the y value in the table

By Graphical method:

A plot of the values given in the table gives the following graph:

The above graph shows a parabola, which is obtained from quadratic functions.

Again, this points us to the conclusion that the parent function is f(x) = x^2

Thus, the answer is: option A

$f(x)=x^2$