Unit 3 test Correction

Consider the expression below: (2^3). What is another way to represent this value? Choose ALL that are correct.

• ( -2 ) + ( -2 ) + ( -2 ) - This results from thinking that a negative exponent represents repeated addition of the negative value of the base.

• ( -2 ) * ( -2 ) * ( -2 ) - This results from thinking that the negative exponent means to apply the negative sign to the base and then use it as a factor with the number of times indicated by the positive value of the exponent.

• 2 * 2 * 2 - This results from failing to realize that a negative exponent does not mean the same thing as a positive exponent.

• 2 * 2 * 2 - A negative exponent means to write a fraction whose numerator is 1 and whose denominator is the base raised to the positive value of the exponent.

• ( 1/2 * 1/2 * 1/2 ) - A negative exponent means to write a fraction whose numerator is 1 and whose denominator is the base raised to the positive value of the exponent.

The graph below shows how the vibration frequency of a certain guitar string varies with tension when its length is held constant. Which function could describe f(x), the vibration frequency in hertz, of the guitar string when its tension is x pounds?

• f(x) = a^x

• f(x) = a√x

• f(x) = ax^3

• f(x) = ax^2

Solve for the following equation. Check for extraneous roots: (9 - 3x)^2 = -6. Provide the solution for x.

Consider the graph of the function f(x) = sqrt(x - 2) below.

• The function is decreasing for all values of x smaller than 2.

• The function does not reach a maximum value.

• The minimum value of f(x) occurs at the point x = 0.

• For some values of x, f(x) < 0.

The speed in miles per hour that a car is traveling when it goes into a skid can be estimated by using the formula ( s = sqrt{30fd} ) where ( f ) is the coefficient of friction and ( d ) is the length of the skid marks in feet. After an accident, a driver claims to have been traveling the speed limit of 55 miles per hour. The coefficient of friction under accident conditions was 0.8. Is the driver telling the truth about his speed if the length of the actual skid marks is 125 feet?

• A. Yes

• B. No

In the graph below, g(x) is the result of a transformation of f(x). If the equation f(x) = √x describes f(x), what equation describes g(x)? Type your response in the box below.

Simplify the expression:
(y²)⁵

• y¹⁰

• y⁷

• y⁵

• y²

 $\left(ab^2\right)^8$  =

•  $ab^{16}$  

•  $a^8b^{16}$  

•  $a^9b^{10}$  

•  $ab^{10}$  

a number, y, to the power of 4

• 4y

• y⁴

• 4

• 4x

Find the equivalent expression for:

x³

• x ⋅ x ⋅ x

• x + x + x

• 3 + 3 + 3

• 3 ⋅ 3 ⋅ 3