Math 1111 Test 3 Review

Math 1111 Test 3 Review

by Teresa Fuston

Multiple Choice

Mary and her husband are each starting a saving plan. Mary will initially set aside $75 and then add $30.65 every week to the savings. The amount A (in dollars) saved this way is given by the function A = 75 + 30.65N, where N is the number of weeks she has been saving.

Her husband will not set an initial amount aside but will add $70.55 to the savings every week. The amount B (in dollars) saved using this plan is given by the function B = 70.55N.

Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible.

• T = 176.20N

• T = 75N + 101.20

• T = 75 + 101.20N

• T = 75 - 101.20N

Multiple Choice

Find the difference quotient   $$\frac{f\left(x-h\right)-f\left(x\right)}{h}$$  ,

where h ≠ 0, for the function below.

$$f\left(x\right)=3x^2−3$$  

Simplify your answer as much as possible.

• -6x + 3

• -6x + 3h

• 3h

• h

Multiple Choice

Suppose that the functions r and s are defined for all real numbers x as follows.

$$r\left(x\right)=3x+2$$  

$$s\left(x\right)=6x-2$$  

Write the expressions for $$\left(s-r\right)\left(x\right).$$  

• 3x - 4

• 3x

• -3x

• -3x + 4

Multiple Choice

The functions r and s are defined as follows.

$$r\left(x\right)=−2x+1$$  

$$s\left(x\right)=x^2+1$$  

Find the value of $$s\left(r\left(4\right)\right)$$  .

• 50

• -33

• -48

• none of these

Multiple Choice

The functions r and s are defined as follows.

$$r\left(x\right)=x+2$$  

$$s\left(x\right)=x^2+1$$  

Find the value of $$s\left(r\left(x\right)\right)$$  .

• $$x^2+3$$  

• $$x^2+4x+5$$  

• $$x^2+5$$  

Multiple Choice

Suppose that the functions f and g are defined as follows.

$$f\left(x\right)=x-4$$  

$$g\left(x\right)=7x−5$$  

Find all values that are NOT in the domain of $$\frac{f}{g}$$  .

• $$x\ne4,\ x\ne\frac{5}{7}$$  

• $$x\ne\frac{5}{7}$$

• $$x\ne4$$

• $$x\ne-4,\ x\ne-\frac{5}{7}$$

Multiple Choice

Suppose $$H\left(x\right)=\sqrt[3]{4x-3}$$  .

Find two functions f and g such that $$f\left(g\left(x\right)\right)=H\left(x\right)$$  .

• $$g\left(x\right)=\sqrt[3]{x}$$  

  $$f\left(x\right)=4x-3$$  

• $$g\left(x\right)=4x-3$$   $$f\left(x\right)=\sqrt[3]{x}$$  

• $$f\left(x\right)=\sqrt[3]{4x}$$   $$g\left(x\right)=-3$$  

Multiple Choice

Suppose the value  of R(d) in d dollars in euros is given by $$R\left(d\right)=\frac{8}{9}d$$  .

The cost P(n) in dollars to purchase and ship n purses is given by $$P\left(n\right)=81n+27$$  . Write a formula for the cost Q(n) in euros to purchase and ship n purses.

• $$Q\left(n\right)=72n+27$$

• $$Q\left(n\right)=9n+3$$  

• $$Q\left(n\right)=9n+27$$  

• $$Q\left(n\right)=72n+24$$

​Answer on paper ...

​(a)  Find the coordinates of the vertex. 

(b)  Find the equation of the axis of symmetry. 

(c)  Find the x-intercept(s). 

(d)  Find the y-intercept(s). 

​

​Check your answers on the next slide!

Multiple Choice

Find the vertex of $$y=x^2−8x+11$$  .

• (-4, 59)

• (4, -5)

• (4, 5)

• (-4, 5)

Multiple Choice

A vehicle factory manufactures boats. The unit cost C (the cost in dollars to make each boat) depends on the number of boats made. If x boats

are made, then the unit cost is given by the function $$C\left(x\right)=0.5x^2−280x+52,500$$  . What is the minimum unit cost?

• $280

• $56

• $13,300

• $38,388

Multiple Choice

Find all the zeros of the quadratic function.

$$y=x^2+8x+12$$  

• 2, 6

• -2, -6

• 3, 4

• -3, -4

Multiple Choice

Consider the polynomial function $$f\left(x\right)=−\left(x+2\right)\left(x+1\right)^2\left(x−1\right)^2$$  .

Determine the end behavior.

• Falls to the left and rises to the right

• Rises to the left and falls to the right

• Rises to the left and rises to the right

• Falls to the left and falls to the right

Multiple Choice

Consider the polynomial function $$f\left(x\right)=−\left(x+2\right)\left(x+1\right)^2\left(x−1\right)^2$$  .

Find the zero(s) where the graph touches, but does not cross the x-axis:

• -1, 1

• -2

Multiple Choice

Consider the polynomial function $$f\left(x\right)=−\left(x+2\right)\left(x+1\right)^2\left(x−1\right)^2$$  .

Find the y-intercept.

• (0, 2)

• (0, 0)

• (0, -1)

• (0, -2)

Multiple Choice

Choose the graph of the function from the choices below.

$$f\left(x\right)=\left(x-3\right)^2\left(x+1\right)\left(x-1\right)$$  

Multiple Select

Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.

Over which intervals is the function decreasing? Choose all that apply.

• $$\left(-\infty,\ -5\right)$$  

• $$\left(-3,\ 0\right)$$  

• $$\left(3,\ 6\right)$$  

• $$\left(6,\ 8\right)$$  

Multiple Select

Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.

At which x-values does the function have local minima? Choose all that apply.

• -5

• -3

• 0

• 6

Multiple Choice

Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.

What is the sign of the function's leading coefficient?

• positive

• negative

• not enough information

Multiple Choice

Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.

What is the least degree of the polynomial function?

• 5

• 6

• 7

Multiple Choice

Find a polynomial f(x) of degree 3 that has the following zeros.

− 5, 0, 6

Leave your answer in factored form.

• f(x) = x(x - 5)(x + 6)

• f(x) = x(x + 5)(x - 6)

• f(x) = x(x - 5)(x - 6)

• f(x) = x(x + 5)(x + 6)

Multiple Choice

Divide. What is the remainder?

$$\left(12x^3+20x^2+11x+3\right)\div\left(3x+2\right)$$  

• -1

• 5

• 1

• -5

Multiple Choice

For the polynomial below, − 3 is a zero.

$$g\left(x\right)=x^3+3x^2−4x-12$$  

Express g(x) as a product of linear factors.

• g(x) = (x-3)(x-2)(x+2)

• g(x) = (x+3)(x-2)(x+2)

• g(x) = (x-3)(x-4)(x+4)

Multiple Choice

The graph of a rational function f is shown below.

Assume that all asymptotes and intercepts are shown and that the graph has no "holes".

Write the equations for all asymptotes.

• x = 0

  y = -3

• x = 0

  x = -3

• x = -3

  y = 0

• y = 0

  y = -3

Multiple Choice

Identify all vertical and horizontal asymptotes of the rational function.

$$f\left(x\right)=\frac{x^2+2x+3}{x^2-4}$$  

• x = 4

  y = 1

• x = 2

  y = 1

• x = 2

  x = -2

  y = 0

• x = 2

  x = -2

  y = 1

​Graph the rational function on paper.

Graph the solution to the following inequality on the number line.

​

​

​

​Check your answer on the next slide.

Multiple Select

Select all of the functions that are one-to-one.

Multiple Choice

Consider the function $$h\left(x\right)=2x-9$$  .

Find $$h^{-1}\left(x\right).$$  

• $$h^{-1}\left(x\right)=2x+9$$  

• $$h^{-1}\left(x\right)=\frac{1}{2}x+9$$  

• $$h^{-1}\left(x\right)=x+\frac{9}{2}$$  

• $$h^{-1}\left(x\right)=\frac{x+9}{2}$$  

Multiple Choice

Graph the function.

$$y=4^x$$  

Multiple Choice

A can of soda is placed inside a cooler. As the soda cools, its temperature               in degrees Celsius is given by the following function T(x), where x

is the number of minutes since the can was placed in the cooler.

$$T\left(x\right)=−7+31e^{−0.041x}$$  

Find the temperature of the soda after 15 minutes.

• $$9.8\degree C$$  

• $$439\degree C$$  

• $$-5.4\degree C$$  

• $$-6.9\degree C$$  

Multiple Choice

An initial amount of $2200 is invested in an account at an interest rate of 6% per year, compounded continuously. Assuming that no withdrawals are made, find the amount in the account after five years.

Do not round any intermediate computations, and round your answer to the nearest cent.

• $2944.10

• $2969.69

• $2963.08

• $2967.47

Multiple Choice

Rewrite as an logarithmic equation.

$$5^{-2}=\frac{1}{25}$$  

• $$\log_{-2}\frac{1}{25}=5$$  

• $$\log_5-2=25$$  

• $$\log_5\frac{1}{25}=-2$$  

• $$\log_{25}5=-2$$  

​Graph the logarithmic function on paper.

​Check your answer on the next slide.

Multiple Choice

Write the expression as a single logarithm.

$$4\log_2w−\frac{1}{2}\log_2z-3\log_2x$$  

• $$\log_2\ \frac{w^4x^3}{\sqrt[]{z}}$$  

• $$\log_2\ \frac{x^3\sqrt[]{z}}{w^4}$$  

• $$\log_2\ \frac{w^4}{x^3\sqrt[]{z}}$$  

• $$\log_2\left(w^4x^3\sqrt[]{z}\right)$$