Question

in exercises 1 - 6, determine whether the equation represents an exponential function. explain.
1.
2.
3.
4.

1. ( y = 6(0.5)^{x}-4 )

6.

in exercises 7 - 10, determine whether the table represents a linear or an exponential function. explain.
7.

x	y
2	0
3	2
4	4

8.

x	y
2	12
3	24
4	48

9.

x	-1	0	1	2	3

10.

x	-3	0	3	6	9

in exercises 11 - 18, evaluate the function for the given value of ( x ).

1. ( y = 9^{x}, x = 2 )
2. ( f(x)=3(2)^{x}, x=-1 )
3. ( y=-4(5)^{x}, x = 2 )
4. ( f(x)=0.5^{x}, x=-3 )
5. ( f(x)=\frac{1}{3}(6)^{x}, x = 3 )
6. ( y=\frac{1}{3}(4)^{x}, x=\frac{1}{2} )
7. ( f(x)=-18(9)^{x}, x=-\frac{1}{2} )
8. ( f(x)=8(9)^{x}, x=\frac{2}{3} )

in exercises 19 and 20, the table represents an exponential function. graph the function.
19.

x	-3	-1	0	3

20.

x	1	3	5	7

6.3 exponential functions 513

Explanation:

Let's solve Exercise 11 as an example. The function is \( y = 9^x \) and we need to evaluate it for \( x = 2 \).

Step 1: Substitute \( x = 2 \) into the function

We have the function \( y = 9^x \). When \( x = 2 \), we substitute \( x \) with 2, so the expression becomes \( y = 9^2 \).

Step 2: Calculate \( 9^2 \)

Recall that \( a^n \) means multiplying \( a \) by itself \( n \) times. So \( 9^2 = 9\times9 = 81 \).

Answer:

81