Question

Dwight creates a table of values for a function and plots the points. He finds that one y value divided by the next y value produces the same answer each time. What kind of function did he graph?
A.) linear
B.) quadratic
C.) square root
D.) exponential

Answer 1

we know that

The exponential function is of the form

$f(x)=a^{x}$

where

a is any value greater than $0$

In General:

It is always greater than $0$, and never crosses the x-axis

It always intersects the y-axis at $y=1$

Its Domain is the Real Numbers

Its Range is the Positive Real Numbers

Examples

Let

$a=3$

1) For $x=2$

$f(2)=3^{2} \\ f(2)=9$

2) For $x=3$

$f(3)=3^{3} \\ f(3)=27$

3) For $x=4$

$f(4)=3^{4} \\ f(4)=81$

4) For $x=5$

$f(5)=3^{5} \\ f(5)=243$

$f(3)/f(2)=\frac{27}{9} \\ =3$

$f(4)/f(3)=\frac{81}{27} \\ =3$

$f(5)/f(4)=\frac{243}{81} \\ =3$

therefore

the answer is the option

D.) exponential

Answer 2

Answer:

we know that

The exponential function is of the form

where

a is any value greater than

In General:

It is always greater than , and never crosses the x-axis

It always intersects the y-axis at

Its Domain is the Real Numbers

Its Range is the Positive Real Numbers

Examples

Let

1) For

2) For

3) For

4) For

therefore

the answer is the option

D.) exponential