Diagnostic Test

1. Jeri is a hairdresser. The table shows the relationship between the number of clients she has per month, x, and her monthly revenue, f(x). Based on the relationship shown in the table, which function represents the situation?

• f(x) = 4x + 720

• f(x) = 12x - 144

• f(x) = 8x - 96

• f(x) = 100x - 1200

2. Each statement describes a transformation of the graph of y = x². Which statement correctly describes the graph of y = (x + 4)² - 7?

• It is the graph of y = x² translated 4 units down and 7 units to the left.

• It is the graph of y = x² translated 7 units down and 4 units to the left.

• It is the graph of y = x² translated 4 units up and 7 units to the left.

• It is the graph of y = x² translated 7 units down and 4 units to the right.

3. Compare the functions below which are represented in the table, and get the write statement.

f(x) = 8x + 3

g(x)= 3^x

• As x increases, the rate of change of f(x) exceeds the rate of change of g(x).

• As x increases, the rate of change of g(x) exceeds the rate of change of f(x).

• At x = 3, the rate of change of g(x) is equal to the rate of change of f(x).

• For every value of x, the rate of change of f(x) exceeds the rate of change of g(x).

4. Pizza PDQ hosted two pizza parties last Friday. The number of slices of pizza eaten by partygoers is displayed on the dot plots. Based on this data, which of the following generalizations can be made?

• The medians and means of both data sets are close to or equal to 3.

• Each data set has a mean of 3. The medians are not equal.

• Each data set has a mean of 3. Each data set has a median of 3.

• The medians and means of both data sets are not close in value.

5. The following formula can be used to find the period of a simple pendulum. If the pendulum length (L) is in meters, and gravity (g) is in meters per second squared, then in what unit is the pendulum period (T) measured?

• seconds per meter

• meters

• seconds

• seconds squared

6. Which of the following shows that the sum of two irrational numbers can be rational?

•  $\left(5\ +\pi\right)+\left(2-\pi\right)$  

•  $\ \frac{\pi}{2\ }\ +\ \frac{\pi}{4}$  

•  $\ \left(\sqrt{5}+2\right)-\left(1-\sqrt{5}\right)$  

•  $\ \frac{\sqrt{2}}{3}+\frac{3}{\sqrt{2}}$  

7. Find the value of f(-1) for the function below.

 $f\left(x\right)=\frac{2}{3}\cdot3^{\left(3x+12\right)}$  

• 19,683

• 13,122

• 512

• 118,098

8.Teddy has 23 boxes of juice packed and plans to pack 3 additional boxes each hour. Charley has 7 boxes packed and plans to pack 5 additional boxes each hour.

After how many hours will Charley have packed the same number of boxes of juice as Teddy?

• 15

• 8

• 2

• Neither

9. Li and Jen went shopping.

• Li bought 5 pairs of earrings and 1 necklace for a total of $75.

• Jen bought 1 pair of earrings and 2 necklaces for a total of $60.

Each pair of earrings cost e dollars and each necklace cost n dollars. Which system of equations can be used to find the cost, in dollars, of each pair of earrings and each necklace?

• 5e + n = $75

  e + 2n = $60

• 5e + 2n = $75

  e + n = $60

• 5e + n = $75

  2e + n = $60

• e + 5n = $75

  e + 2n = $60

10.Re-write the expression using rational exponents.

 $\sqrt{7y^3}$  

•  $7y^{\frac{3}{2}}$  

•  $7y^{\frac{2}{3}}$  

•  $7^{\frac{1}{2}}y^{\frac{2}{3}}$  

•  $7^{\frac{1}{2}}y^{\frac{3}{2}}$