Answer to Question #264447 in Algebra for Elis

Question

Find the domain and range of the following exponential functions:

1. 𝑓(𝑥) = (

1

2

)

𝑥+1

6. 𝑓(𝑥) = 2

𝑥−1 + 1

2. 𝑓(𝑥) = 3

𝑥+2 7. 𝑓(𝑥) = −5

𝑥 − 2

3. 𝑓(𝑥) = −(5)

𝑥 8. 𝑓(𝑥) = (

1

4

)

2𝑥+1

+ 3

4. (𝑥) = 4

−𝑥 9. 𝑓(𝑥) = 5

3𝑥 − 4

5. (𝑥) = (

1

3

)

−𝑥+1

10. 𝑓(𝑥) = − (

2

3

)

𝑥

− 3

Answer 1

1. $f(x)=(\dfrac{1}{2})^x$

Domain: $(-\infin, \infin)$

Range: $(0, \infin)$

2. $f(x)=3^{x+2}$

Domain: $(-\infin, \infin)$

Range: $(0, \infin)$

3. $f(x)=-(5)^{x}$

Domain: $(-\infin, \infin)$

Range: $(-\infin, 0)$

4. $f(x)=4^{-x}$

Domain: $(-\infin, \infin)$

Range: $(0, \infin)$

5. $f(x)=(\dfrac{1}{3})^{-x+1}$

Domain: $(-\infin, \infin)$

Range: $(0, \infin)$

6. $f(x)=2^{x-1}+1$

Domain: $(-\infin, \infin)$

Range: $(1, \infin)$

7. $f(x)=-5^{x}-2$

Domain: $(-\infin, \infin)$

Range: $(-\infin, -2)$

8. $f(x)=(\dfrac{1}{4})^{2x+1}+3$

Domain: $(-\infin, \infin)$

Range: $(3, \infin)$

9. $f(x)=5^{3x}-4$

Domain: $(-\infin, \infin)$

Range: $( -4, \infin)$

10. $f(x)=-(\dfrac{2}{3})^{x}-3$

Domain: $(-\infin, \infin)$

Range: $(-\infin, -3)$