# Expert Answers

1. Which of these graphs represent a one-to-one function?

A one-to-one function must pass both the Vertical Line Test and the Horizontal Line Test.

Graphs B and D fail the Horizontal Line Test, and Graph C fails the Vertical Line Test.

The only graph which passes both tests is Graph A.

2. The students in history class took a final exam and then took equivalent forms of the exam at monthly intervals thereafter. The average store S(t), as percent, after t months was found to be given by:

S(t) = 78 – 15log(t + 1), t ≥ 0

(a) What was the average score when the students initially took the test, t = 0?

(b) What was the average score after 4 months?

3. Convert to a logarithmic equation: 5x = 251

A. log5 251 = x

B. logx 251 = 5

D. logx 5 = 251

D. log5 x = 251

4. Solve the equation. Check all proposed solutions.

5. Simplify:

(a) log8 1

(b) log5 (1/625) = log5(1/54) = log5(5-4) = -4 * log55 = -4 * 1 = -4

6. Let f(x) = e x + 1 – 3.

(a) Which describes how the graph of f can be obtained from the graph of y = ex?

(b) What is the domain of f ?

(c) What is the range of f ?

(d) Sketch the graph of f.

7. Quadratic Polynomial of Best Fit:

(a) Using algebraic techniques we have learned, find the maximum temperature predicted by the quadratic model and find the time when it occurred. Report the time to the nearest quarter hour (i.e. __:00 or __:15 or __:30 or __:45). (For instance, a time of 18.25 hours is reported as 6:15 pm.) Report the maximum temperature to the nearest tenth of a degree.

(b) Use the quadratic polynomial to estimate the outdoor temperature at 9:30 am, to the nearest tenth of a degree.

(c) Use the quadratic polynomial y = -0.3476t2 + 10.948t – 6.0778 together with algebra to estimate the time(s) when the outdoor temperature y was 70 degrees. State your results clearly; report the time(s) to the nearest quarter hour.

8. Let f(x) = 3x + 1 and g(x) = x2 – 2x – 6

(a) Find the composite function (f o g)(x) and simplify the results

(b) Find (f o g)(-2)

(c) Find the composite function (g o f)(x) and simplify the results

(d) Find (g o f)(-2)

9. Let

(a) Find f ‑1, the inverse of f.

(b) What is the domain of f ?

(c) What is the domain of the inverse function?

(d) What is f(2)?

(e) What is f -1(__), where the number in the blank is your answer from part (d)?

10. Exponential Function of Best Fit

y = 89.976 e-0.023t where t = Time Elapsed (minutes) and y = Temperature Difference (in degrees)

Use the exponential function to estimate the coffee temperature C when 35 minutes have elapsed. Report your estimated temperature difference to the nearest tenth of a degree.

A one-to-one function must pass both the Vertical Line Test and the Horizontal Line Test.

Graphs B and D fail the Horizontal Line Test, and Graph C fails the Vertical Line Test.

The only graph which passes both tests is Graph A.

2. The students in history class took a final exam and then took equivalent forms of the exam at monthly intervals thereafter. The average store S(t), as percent, after t months was found to be given by:

S(t) = 78 – 15log(t + 1), t ≥ 0

(a) What was the average score when the students initially took the test, t = 0?

(b) What was the average score after 4 months?

3. Convert to a logarithmic equation: 5x = 251

A. log5 251 = x

B. logx 251 = 5

D. logx 5 = 251

D. log5 x = 251

4. Solve the equation. Check all proposed solutions.

5. Simplify:

(a) log8 1

(b) log5 (1/625) = log5(1/54) = log5(5-4) = -4 * log55 = -4 * 1 = -4

6. Let f(x) = e x + 1 – 3.

(a) Which describes how the graph of f can be obtained from the graph of y = ex?

(b) What is the domain of f ?

(c) What is the range of f ?

(d) Sketch the graph of f.

7. Quadratic Polynomial of Best Fit:

(a) Using algebraic techniques we have learned, find the maximum temperature predicted by the quadratic model and find the time when it occurred. Report the time to the nearest quarter hour (i.e. __:00 or __:15 or __:30 or __:45). (For instance, a time of 18.25 hours is reported as 6:15 pm.) Report the maximum temperature to the nearest tenth of a degree.

(b) Use the quadratic polynomial to estimate the outdoor temperature at 9:30 am, to the nearest tenth of a degree.

(c) Use the quadratic polynomial y = -0.3476t2 + 10.948t – 6.0778 together with algebra to estimate the time(s) when the outdoor temperature y was 70 degrees. State your results clearly; report the time(s) to the nearest quarter hour.

8. Let f(x) = 3x + 1 and g(x) = x2 – 2x – 6

(a) Find the composite function (f o g)(x) and simplify the results

(b) Find (f o g)(-2)

(c) Find the composite function (g o f)(x) and simplify the results

(d) Find (g o f)(-2)

9. Let

(a) Find f ‑1, the inverse of f.

(b) What is the domain of f ?

(c) What is the domain of the inverse function?

(d) What is f(2)?

(e) What is f -1(__), where the number in the blank is your answer from part (d)?

10. Exponential Function of Best Fit

y = 89.976 e-0.023t where t = Time Elapsed (minutes) and y = Temperature Difference (in degrees)

Use the exponential function to estimate the coffee temperature C when 35 minutes have elapsed. Report your estimated temperature difference to the nearest tenth of a degree.

You'll get a 494.7KB .DOCX file.