precalculus

25 questions due by 10:15AM

1

. Graph the exponential function by hand. Identify any asymptotes and intercepts and determine whether the graph of the function is increasing or decreasing. (Enter NONE in any unused answer blanks.)

Equation of horizontal asymptote:

 

Equation of

vertical asymptote

:
 

Value of y-intercept
 
Value of x-intercept
 
The function is

2

. Use the graph of y 

=

 

2x to match the function with its graph.

A

B

C

D

y = 2x – 4

  

  

y = 2x – 5

    

y = 2x + 4

    

y = 2–x

    

3

. Use the graph of f to describe the transformation that yields the graph of g. Then sketch the graphs of f and g by hand.

f(x) = −2x, g(x) = 5 − 2x

The graph of g(x) = 5 − 2x is a vertical shift five units downward of f(x) = −2x.

The graph of g(x) = 5 − 2x is a horizontal shift five units to the left of f(x) = −2x.

    

The graph of g(x) = 5 − 2x is a vertical shift five units upward of f(x) = −2x.

The graph of g(x) = 5 − 2x is a horizontal shift five units to the right of f(x) = −2x.

Sketch the graphs of f and g.

4. Use a graphing utility to construct a table of values for the function. (Round your answers to three decimal places.)

			x	f(x) = 5x − 3
	-1
	0
	1
2
3

Sketch the graph of the function.

Identify any asymptotes of the graph. (Enter NONE in any unused answer blanks.)

x

= 

	vertical asymptote				=
	horizontal asymptote		y

5. Use a graphing utility to construct a table of values for the function. (Round your answers to three decimal places.)

x

-1

0

g(x) = 4 − e−3x

-4

-3

-2

Sketch the graph of the function.

 

Identify any asymptotes of the graph. (Enter NONE in any unused answer blanks.)

vertical asymptote

x

= 

horizontal asymptote    

y

= 

6. Fill in the blank.

If 

x = 

ey,

 then y =  .

7. For what value of x is 

ln

 x = ln 9?

x = 

8. Write the

log

arithmic equation in exponential form. For example, the exponential form of 

log5 25 = 2 is 52 = 25.

log2 512 = 9

					=

9. Write the logarithmic equation in exponential form. For example, the exponential form of log5 25 = 2 is 52 = 25.

log 

1

100,000,000

 = -8

 
 

=

10. Write the exponential equation in logarithmic form. For example, the logarithmic form of 

23 = 8 is log2(8) = 3.

43/2 = 8

log

  

= 

11. Use a calculator to evaluate the function at the indicated value of x. Round your result to three decimal places.

f(x) = log10(x)                x = 4/5

12. Solve the equation for x.

log10(102) = x

13. Write the logarithmic equation in exponential form. For example, the exponential form of ln(5) = 1.6094… is e1.6094… = 5. (Do not use … in your answer.)

 

 
 

=

14. Write the exponential equation in logarithmic form. For example, the logarithmic form of 

e2 = 7.3890    is ln 7.3890  

  =

2.

 (Do not use … in your answer.)

e2.2 = 9.0250  

ln   =

15. Use the properties of natural logarithms to rewrite the expression. 5 ln(e5) 16. Use the properties of logarithms to rewrite and simplify the logarithmic expression. ln 9 e9     17. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) log9(9x)  18. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) ln 7 t 19. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) ln x4 y3   20. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) ln x2 − 4 x8 ,  x > 2 21. Condense the expression to the logarithm of a single quantity. 5 ln x + 2 ln y − 3 ln z   22. Use a graphing utility to graph the function and approximate its zero accurate to three decimal places. h(t) = e0.125t − 3 t =  23. Solve the logarithmic equation algebraically. Round the result to three decimal places. Verify your answer using a graphing utility. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) ln 9x = 1.6 x =   24. Use the zero or root feature of a graphing utility to approximate the solution of the logarithmic equation. (Enter your answers as a comma-separated list. Round your answers to three decimal places.) ln x + ln(x2 + 4) = 11 x =   25. Use a graphing utility to approximate the point of intersection of the graphs. Round your result to three decimal places. y1 = 1.03 y2 = ln  x − 4 (x, y) =