12.4.A.1Multiple Choice
Which expression is equivalent to 2x+4 for every x?
Select A, B, C, or D to check your answer.
Directions: Work each problem on your own paper first. For multiple choice, select A, B, C, or D. You will see right away whether you are correct. If you miss, you will see the most likely reason, and you can try again. For short response, type your answer, then compare it with the model solution. Questions 1–8 go through 2.4.A.1–A.4 in order; questions 9–20 mix them. Check rewritten forms by testing one input in both versions. Round sensibly: other decimals to the nearest thousandth.
Which expression is equivalent to 2x+4 for every x?
Select A, B, C, or D to check your answer.
Let f(x) = 3x+2. (a) Rewrite f in the form abx. (b) State the initial value. (c) Check your form at x = 1.
Which function is equivalent to f(x) = 23x?
Select A, B, C, or D to check your answer.
Rewrite each function as an exponential function with a single base. (a) g(x) = 9x/2 (b) h(x) = 43x (c) Check both at x = 2.
What is the value of 4−2?
Select A, B, C, or D to check your answer.
Let f(x) = 8·2−x. (a) Rewrite f in the form abx. (b) Is it exponential growth or decay? (c) Find f(3) and f(−2).
What is the value of 641/3?
Select A, B, C, or D to check your answer.
Evaluate each without a calculator. (a) 811/4 (b) 82/3 (c) 25−1/2 (d) 272/3
A quantity is modeled by f(d) = 3d/2, where d is the number of days. Which equivalent function shows the factor the quantity is multiplied by each day?
Select A, B, C, or D to check your answer.
A medicine in the body is modeled by A(t) = 80·(1/2)t/6 mg after t hours. (a) How long does it take for the amount to halve? (b) Rewrite A in the form a·bt. (c) What percent of the medicine is removed each hour? (d) Find A(12), using both forms.
Which function is equivalent to g(x) = 7·3x−1?
Select A, B, C, or D to check your answer.
Let k(x) = (1/4)x/2. (a) Rewrite k with a single base of the form bx. (b) Is it growth or decay? (c) Check both forms at x = 4.
Which function demonstrates exponential decay?
Select A, B, C, or D to check your answer.
Which is equal to 3−2 · 35?
Select A, B, C, or D to check your answer.
A cell culture is modeled by Q(t) = 40·2t/4 cells after t hours. (a) How long does it take to double? (b) Rewrite Q in the form a·bt. (c) By about what percent does it grow each hour? (d) Find Q(8).
The graph of f(x) = 2x−3 is the graph of 2x shifted 3 units to the right. (a) Show that f is also a vertical dilation of 2x. By what factor? (b) Complete the check: compare f(x) and the dilated form at x = 3, 4, 5.
| x | 3 | 4 | 5 |
| 2x−3 | 1 | 2 | 4 |
Which expression is equivalent to (1/3)x?
Select A, B, C, or D to check your answer.
Let f(x) = 12·4−x/2. (a) Rewrite f in the form abx. (b) Is it growth or decay? (c) Find f(2) and f(6).
Which statement about (−16)1/4 is true?
Select A, B, C, or D to check your answer.
A bacteria sample is modeled by N(t) = 250·3t/2 after t hours. (a) Rewrite N(t) in the form a·bt, and give b exactly and as a decimal. (b) By about what percent does the sample grow each hour? (c) Find N(4) from both forms. (d) By what factor does the sample grow every 4 hours?