Question

The tables represent the functions f(x) and g(x).A table showing g(x) equals 2 x plus 15 with 2 columns and 7 rows. The first column, x, has the entries, negative 15, negative 12, negative 9, negative 6, negative 3, 0. The second column, g(x), has the entries, negative 15, blank, blank, blank, blank, 15.Which input value produces the same output value for the two functions?

Answer 1

x=-6

Explanation

to solve this, let´s complete the tables and then compare

Step 1

complete the table:

to do that we need to input the x value and evaluate to obtain f(x)

so

a) for

$f(x)=\frac{2}{3}x+7$

i)when x=-12

$\begin{gathered} f(-12)=\frac{2}{3}(-12)+7 \\ f(-12)=-8+7=-1 \\ f(-12)=-1 \\ so \\ (-12,-1) \end{gathered}$

ii) when x= -9

$\begin{gathered} f(-9)=\frac{2}{3}(-9)+7 \\ f(-9)=-6+7=1 \\ f(-9)=1 \\ so \\ (-9,1) \end{gathered}$

iii) when x=-6

$\begin{gathered} f(-6)=\frac{2}{3}(-6)+7 \\ f(-6)=-4+7=3 \\ f(-6)=3 \\ so \\ (-6,3) \end{gathered}$

iv) when x= -3

$\begin{gathered} f(-3)=\frac{2}{3}(-3)+7 \\ f(-3)=-2+7=5 \\ f(-3)=5 \\ so \\ (-3,5) \end{gathered}$

hence

Step 2

Now , for equation(2) g(x)

$g(x)=2x+15$

a) when x=-12

$\begin{gathered} g(x)=2x+15 \\ g(-12)=2(-12)+15=-24+15=-9 \\ g(-12)=-9 \end{gathered}$

b) when x=-9

$\begin{gathered} g(x)=2x+15 \\ g(-9)=2(-9)+15=-18+15=-3 \\ g(-9)=9 \end{gathered}$

c) when x=-6

$\begin{gathered} g(x)=2x+15 \\ g(-6)=2(-6)+15=-12+15=3 \\ g(-6)=3 \end{gathered}$

d)when x=-3

$\begin{gathered} g(x)=2x+15 \\ g(-3)=2(-3)+15=-6+15=9 \\ g(-3)=9 \end{gathered}$

so

Step 3

finally, compare and check wich input value produces the same out put

therefore, the answer is

x=-6

I hope this helps you