Answers KISD SS-3391B-Algebra II Honors BModeling with Rational Functions

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The resistance, R, to electricity of a cylindrical-shaped wire is given by the equation , where p represents the resistivity of the wire’s material, L represents the length of the wire, and d represents the diameter of the wire. What happens to the resistance of the wire as the diameter approaches 0?

The resistance approaches 0.

The resistance approaches .

The resistance approaches L.

The resistance approaches infinity.

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Which expression is equivalent to the following complex fraction?

StartFraction y + x Over y minus x EndFraction

StartFraction (y minus x) (y + x) Over x squared y squared EndFraction

StartFraction x squared y squared Over (y + x) (y + x) EndFraction

StartFraction y minus x Over y + x EndFraction

Riley makes a mistake in step 2 while doing her homework. What was her mistake? Step 1: Step 2: Step 3: Step 4:

She added the two fractions incorrectly.

She used the wrong common denominator.

She did not distribute the negative correctly.

She did not multiply the first fraction by a factor.

For the inverse variation equation xy = k, what is the constant of variation, k, when x = –2 and y = 5?

–10

Negative two-fifths

Five-halves

The quantity n varies jointly with the product of z and the square of the sum of x and y. When x = 2, y = 1, and z = 3, n = 18. What is the constant of variation?

One-ninth

Two-thirds

Six-fifths

Which graph represents the function ?

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 3, and the horizontal asymptote is at y = negative 2.

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens down and to the left in quadrants 2 and 3. A vertical asymptote is at x = 3, and the horizontal asymptote is at y = negative 2.

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens down and to the left in quadrants 2 and 3. A vertical asymptote is at x = negative 3, and the horizontal asymptote is at y = 2.

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1 , and the other curve opens down and to the left in quadrants 2, 1, and 4. A vertical asymptote is at x = 3, and the horizontal asymptote is at y = 2.

Which expression is equivalent to the expression below?

StartFraction 3 c (2 c minus 1) Over 2 c + 1 EndFraction

StartFraction negative 3 c (2 c + 1) squared Over 4 (2 c minus 1) squared EndFraction

–3c

Which solution to the equation is extraneous?

a = –2

a = –2 and a = 4

neither a = –2 nor a = 4

a = 4

For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1?

a = –1, m = 0

a = 1, m = 0

a = –1, m = 1

a = 1, m = 1

Which statement is true about the discontinuities of the function f(x)?

There is a hole at x = 2.

There are asymptotes at x = 0 and x = –1.

There are asymptotes at x = 0 and x = –1 and a hole at .

There are holes at x = 0 and x = –1 and an asymptote at x = 2.

For the inverse variation equation , what is the value of p when V = ?

StartFraction 1 Over 32 EndFraction

One-half

Which expressions are equivalent to ?

2–10 and

10–2 and

10–10 and

Which expression is equivalent to the following complex fraction?

StartFraction x minus 3 Over x EndFraction

StartFraction x + 3 Over 1 EndFraction

StartFraction x + 3 Over x EndFraction

StartFraction x Over x + 3 EndFraction

Which statement comparing the oblique asymptotes of the functions f(x) and g(x) is true?

The oblique asymptote for g(x) is steeper than for f(x).

Both functions have the same oblique asymptote.

The oblique asymptote for f(x) is steeper than for g(x).

Both functions have parallel oblique asymptotes.

What is the solution to the equation ?

m = –4

m = –2

m = 2

m = 4

Tyna simplified the expression to . What was Tyna’s mistake?

She divided the coefficients incorrectly.

She added the exponents instead of subtracting them.

She divided the coefficients instead of subtracting them.

She subtracted the exponents instead of dividing them.

Using V = lwh, what is an expression for the volume of the following rectangular prism?

StartFraction 15 Over 2 x EndFraction

StartFraction 3 x + 12 Over 2 x + 8 EndFraction

StartFraction 15 Over 2 x + 2 EndFraction

Fifteen-eighths

Haji rows his canoe 10 mph in still water. He noticed one day that he could row 4 miles upstream in the same amount of time he could row 6 miles downstream. What was the approximate speed of the current that day?

2.0 mph

3.3 mph

5.0 mph

10.0 mph

Which statements comparing the graphs of function 1 and function 2 are true? Check all that apply.

Function 1 has a hole, while function 2 does not.

Function 1 has an oblique asymptote, while function 2 does not.

Function 2 has a hole, while function 1 only has asymptotes.

Function 2 only has asymptotes, while function 1 has a hole.

Both functions have the same domain restriction.

Both functions have the same vertical asymptote.

A certain company has a fixed cost of $200 per day. It costs the company $3.10 per unit to make its products. The company is tracking its average cost to make x units using . Which statement is true?

The horizontal asymptote of y = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.

The horizontal asymptote of y = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.

The vertical asymptote of x = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.

The vertical asymptote of x = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.

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