Math Final Multiple Choice

Identify the y-int of the graph of R(x)=6(x−1)/(x+1)(x+2)

-3

Given f(x)=4x^4−2x^3+7x−2, how many sign changes are in the coefficients of f(−x).f(−x)

1

The average cost per hour in dollars, of producing x riding lawn mower can be modeled by f(x)=0.3x2+21x−251+2500xf(x)=0.3x2+21x−251+x2500​ Use your graphing calculator to determine the number of lawn mowers to produce in order to minimize the average cost.

10

A ball is thrown vertically upwards with an initial velocity of 80 ft/second. The distance s, in feet, of the ball from the ground is given by s(t)=80t−16t^2, where t is in seconds. What is the maximum height?

100

In April 2018, Nicor Gas had the following rate schedule for small businesses. Monthly Charge: $90.00 Distribution charges: First 150 therms: $0.1201/therm Next 4850 therms: $0.0549/therm Over 5000 therms: $0.0482/therm Gas Supply Charge: &0.35/therm What is the charge for using 6000 therms in a month? Round your answer to two decimal places if necessary.

2,522.48

A ball is thrown vertically upwards with an initial velocity of 80 ft/second. The distance s, in feet, of the ball from the ground is given by s(t)=80t−16t^2, where t is in seconds. Exactly after how many seconds the ball reaches its maximum height?

2.5

Refer to question 26. What is the minimum average cost?

239

A lawn mower manufacturer has found the revenue in dollars from sales of zero-turn mower is a function of unit price p, in dollars, if the revenue is R(x)=−1/2p^2+2900p, what unit price p should be charged to maximize revenue? Round your answer to the nearest dollar.

2900

Suppose that the quantity supplied S and the quantity demanded D of hot dog at a baseball game are given by S(p)=−2000+3000p &D(p)=10000−1000p, where p is the price of a hot dog. Find the equilibrium price.

3

f(x) is a piecewise-defined function. f(x)=3x−2,ifx<2.f(x)=x2+5,if2≤x≤10&f(x)=3,ifx>10.f(x)=3x−2,ifx<2.f(x)=x2+5,if2≤x≤10&f(x)=3,ifx>10..Which expression(s) should be used to find the y-intercept?

3x−2

Which of the following could be a test number for the interval -2<x<5

4

A lawn mower manufacturer has found the revenue in dollars from sales of zero-turn mower is a function of unit price p, in dollars, if the revenue is R(x)=−1/2p^2+2900p. What is the maximum revenue? Round your answers to the nearest dollar.

4,205,000

A ball is thrown vertically upwards with an initial velocity of 80 ft/second. The distance s, in feet, of the ball from the ground is given by s(t)=80t−16t^2, where t is in seconds. After how many seconds the ball will strike the ground?

5

Suppose that the quantity supplied S and the quantity demanded D of hot dog at a baseball game are given by S(p)=−2000+3000p &D(p)=10000−1000p, where p is the price of a hot dog. Find the equilibrium price. What is the equilibrium quantity

7,000

Given P1=(−1,3)&P2=(5,−1)P1​=(−1,3)&P2​=(5,−1), find the distance from P1 to P2 (round your answer to two decimals).

7.21

If a graph is symmetric with respect to the x-axis, then it cannot be symmetric with respect to the y-axis.

False

Slope of the line 2y = 3x +5 is 3.

False

The distance between two points is sometimes a negative number.

False

A car has 12500 miles on its odometer. Say the care is driven an average of 40 miles per day. Choose the model that expresses the number of miles N that will be on its odometer after x days.

N(x)= 12500x+40

Determine whether the given relation is a function:∣y∣=2x+3

NOT a function

For a quadratic function whose discriminant is positive, what conclusion can be made about its graph?

The graph has two distinct x-intercepts

If the graph of an equation is symmetric with respect to the origin and (3, -4) is a point on the graph, then (-3, 4) is also a point on the graph.

True

Which type of asymptote will never intersect the graph of a rational function.

Vertical

Given P1=(−1,3)&P2=(5,−1)P1​=(−1,3)&P2​=(5,−1), find the midpoint between P1 to P2 .

m= (x1+x2/2),(y1+y2/2)= (-1+5/2), (3+(-1)/2)= (4/2),(2/2) midpoint= (2,1)

Choose the formula for finding slope of a nonvertical line that contains points (x1, y1) and (x2, y2).

m= ​y1​−y2​​ / x1-x2

If a line slants downward from left to right, then which of the following describes its slope?

negative

The graph of f(x)=ax^2+bx+c has a maximum value at its vertex, which condition must be true?

a<0

Find a polynomial with the given zeros containing the given point: Zeros: -5 (multiplicity 2), 2 (multiplicity 1), 4 (multiplicity 1) and contains point (3, 128)

answer on exam three answer list #22

a) Use your calculator and given data to find a cubic polynomial of third degree. (for part a only round your numbers to 3 decimals). b)Use the function in part a to predict the number of hurricanes in 2011 to 2020.

answer on exam three answer list #23

Solve the inequality algebraically: 3(x−2)^2<(x−1)^2+x^2+2x

answer on exam three answer list #24

The independent variable is sometimes refer to as

argument

Given two functions f and g, the composite function, denoted f o g (f composed of g) is defined by (f o g)(x) = f(g(x)).

composite function

Find a polynomial with real zeros -2, 3, and 5 of degree 3 and contains the point (2, 36)

f(x)= (x+2) (x-3) (x-5) f(x)= a(x+2)(x-3)(x-5) 36= a(4)(2-3)(2-5) 36= 4a(-1)(-3) 36= 4a(3)= 12a 36/12=3 so a=3 f(x)= 3(x+2)(x-3)(x-5)

if x1 and x2 are two different inputs of a function f, then f is one-to-one if _____

f(x1)not equal to f(x2)

A polynomial of degree 4 with the real coefficients could have 3, 3−I, 2+i, and 2−i as its zeros.

false

Domain and range of reciprocal function are the set of all real numbers.

false

Every graph represents a function.

false

Every polynomial of degree 3 with real coefficient has exactly three real zeros.

false

If 3+4i is a zero of a polynomial of odd degree with the real coefficients, then so is 3−4i

false

If r is a real zero of even multiplicity of a polynomial function f, then the graph of f crosses the x-axis at r.

false

If the domain of f and g are the same, then we must have f(x)≥g(x) or f(x)≤g(x) for all x in their domain.

false

If x−▹±∞, and the values of a rational function R(x) approaches some fixed number L, then y = L is a vertical asymptote for the graph of R.

false

Suppose the graph of function f is known. Then the graph of y = f(-x) is reflection about x-axis of the graph of function y = f(x)

false

The average rate of change of y=2x+8 is 8.

false

The average rate of change of y=3x+8 is 8.

false

The cube root function is odd and decreasing on interval (−∞,∞)(−∞,∞)

false

The domain of f/g consists of all numbers x that are in the domain of both f&g.

false

The graph of every rational function has at least one asymptote.

false

The graph of f(x)=x/x−3 is above the x-axis for x<0 or x>3, therefore the solution set for the inequality x/x−3≥0 is {x∣x≤0orx≥3}}{x∣x≤0orx≥3}}

false

The graph of y = - f(x) is the reflection about y-axis of the graph of y = f(x)

false

The lines y = 2x-1 and y = ax +2 are perpendicular if a=1/2

false

The slope of a vertical line is the average rate of change of the line.

false

Two nonvertical lines have slopes of m and n respectively, if m = n, then the lines are parallel and have the same y-intercepts.

false

the graph of y=1/3g(x) is the graph of y=g(x)y=g(x) vertically stretched by a factor of 3.

false

If R(x)=p(x)/q(x) is a rational function and if p and q have no common factors, then R is

in lowest terms

Which one is a type of function that has a constant average rate of change?

linear function

Determine whether the given relation is a function:{(−4,6),(−3,3),(4,9),(−2,2),(5,11),(1,11),(−4,0)}{(−4,6),(−3,3),(4,9),(−2,2),(5,11),(1,11),(−4,0)}

not a function

An odd function is symmetric with respect to

origin

If f(x)=q(x)g(x)+r(x), the function r(x) is called

remainder

The distance between points (a, b) and (c, d)

square root of (c-a)^2 (d-b)^2

Every polynomial function of odd degree with real coefficients will have at least one real zero.

true

For a rational function R, if the degree of numerator is less than the degree of denominator, R is proper.

true

For the parabola f(x)=ax2+bx+c, the line x=−b/2a​ is the axis of symmetry.

true

If R(x) is a rational function and as x−▹c, c is a real number, the values of |R(x)| approaches infinity, then the line x = c is a vertical asymptote.

true

If R(x)=p(x)/q(x)​ is a proper rational function, then y=0 is its horizontal asymptote.

true

If f is a polynomial of degree 4 and if f(2)=5, then f(x)/x−2=p(x)+5/x−2​, where p(x) is a polynomial of degree 3.

true

If the discriminant of f(x)=ax^2+bx+c is zero, then the graph of f touches the x-axis at its vertex.

true

The graph of a rational function may intersect its horizontal asymptote.

true

The midpoint of a line segment can be found by averaging the x-coordinates and y-coordinates of the endpoints.

true

The y-coordinate of of the vertex of f(x)=−x^2+4x+5 is f(2).

true

Which type of asymptote, when it occurs, describes the behavior of a graph when x approaches to some number.

vertical

To test whether the graph of an equation is symmetric with respect to the origin we must replace________ in the equation and simplify. If an equivalent equation results, then the graph is symmetric with respect to the origin.

x by -x and y by -y

The graph of a function y=f(x) can have more than one of which type of intercept?

x-int

Given the intercepts of a graph are (-4, 0) and (0, 5) choose the statement that is true.

x-int is -4 and y-int is 5

Which function has a graph that is the graph of y = f(x) horizontally stretched by a factor of 4.

y=f(1/4x)