Question

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4. Use a graph to determine if the exponential function g( x) = -6 * 5^x is positive or negative and increasing or decreasing.

(A) positive, increasing
(B) positive, decreasing
(C) negative, increasing
(D) Negative, decreasing


6. Which of the exponential functions below has a y
-intercept of 2?
(A) f(x)=3^2x
(B) g(x)=3^x+1
(C) h(x)=3^x+2
(D) j(x)=3*2^x

Answer 1

they answers for Graphing Exponential Functions

1.C

2.C

3.A

4.C

5.C

6.B

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Explanation:

Answer 2

3. The correct option is A.

4. The correct option is C.

5. The correct option is C.

6. The correct option is B.

Explanation:

3.

The given function is

`f(x)=(3)/(2)\cdot ((4)/(5))^x`

`lim_(x\rightarrow -\infty)f(x)=lim_(x\rightarrow -\infty)(3)/(2)\cdot ((4)/(5))^x`

`lim_(x\rightarrow -\infty)f(x)=(3)/(2)\cdot ((4)/(5))^(-\infty)=\infty`

The function approaches to ∞ as x approaches to -∞.

`lim_(x\rightarrow \infty)f(x)=lim_(x\rightarrow \infty)(3)/(2)\cdot ((4)/(5))^x`

`lim_(x\rightarrow \infty)f(x)=(3)/(2)\cdot ((4)/(5))^(\infty)=0`

The function approaches to 0 as x approaches to ∞.

Therefore option A is correct.

4.

The given function is

`g(x)=-6(5)^x`

The exponential function is in the form of

`f(x)=ab^x`

If a<0, then f(x) is a negative function and if a>0, then f(x) is a positive function.

If |b|>1, then f(x) is a increasing function and if |b|<1, then f(x) is a decreasing function.

Since a=-6<0 and b=5>1, therefore f(x) is a negative and increasing function.

Option C is correct.

5.

From the given graph it is noticed that the graph passing through the points (-1,-8) and (1,-2).

We have to find the slope of graph from -1 to 1.

`m=(f(x_2)-f(x_1))/(x_2-x_1)`

Slope of function form -1 to 1 is

`m=(f(1)-f(-1))/(1-(-1))=(-2-(-8))/(1-(-1))=(6)/(2)=3`

Therefore option C is correct.

6.

The y-intercept is 2 it means at x=0, the value of y is 2.

`f(x)=3^(2x)=3^(2(0))=3^0=1`

`g(x)=3^x+1=3^0+1=1+1=2`

`h(x)=3^x+2=3^0+2=1+2=3`

`j(x)=3*2^x=3*2^0=3`

Since g(x) has y-intercept 2, therefore option B is correct.