Graphing Reciprocal Functions Quiz

What is the general form of a reciprocal function?

• y = x

• y = 1 + x

• y = 1/x

• y = x^2

Answer explanation

A reciprocal function has the general form y = 1/x. This choice represents the inverse relationship between x and y, where y is equal to the reciprocal of x.

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

How do you graph a reciprocal function using a table of values?

• Choose x-values and calculate the corresponding y-values by taking the reciprocal of each x-value

• Choose x-values and calculate the corresponding y-values by adding 1 to each x-value

• Choose x-values and calculate the corresponding y-values by squaring each x-value

• Choose x-values and calculate the corresponding y-values by taking the square root of each x-value

Answer explanation

To graph a reciprocal function, choose x-values and calculate the corresponding y-values by taking the reciprocal of each x-value.

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

What are the asymptotes of a reciprocal function and how do you identify them?

• Curved and slanted lines, identified by setting the numerator equal to zero and analyzing the behavior as x approaches positive or negative infinity.

• Horizontal and diagonal lines, identified by setting the numerator equal to zero and analyzing the behavior as x approaches positive or negative infinity.

• Vertical and horizontal lines, identified by setting the denominator equal to zero and analyzing the behavior as x approaches positive or negative infinity.

• Vertical and diagonal lines, identified by setting the denominator equal to zero and analyzing the behavior as x approaches positive or negative infinity.

Answer explanation

The asymptotes of a reciprocal function are vertical and horizontal lines. They are identified by setting the denominator equal to zero and analyzing the behavior as x approaches positive or negative infinity.

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

Explain how to graph a reciprocal function with transformations.

• To graph a reciprocal function with transformations, start by graphing the parent function y = x. Then apply any transformations such as shifts, stretches, or reflections to the graph.

• To graph a reciprocal function with transformations, start by graphing the parent function y = 1/x. Then apply any transformations such as shifts, stretches, or reflections to the graph.

• To graph a reciprocal function with transformations, start by graphing the parent function y = 1/x. Then do not apply any transformations to the graph.

• To graph a reciprocal function with transformations, start by graphing the parent function y = 1/x. Then only apply horizontal transformations to the graph.

Answer explanation

To graph a reciprocal function with transformations, start by graphing the parent function y = 1/x. Then apply transformations like shifts, stretches, or reflections to the graph.

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.BF.B.3

What is the domain of a reciprocal function and how do you find it?

• Only negative numbers

• Only even numbers

• Only prime numbers

• All real numbers except for 0

Answer explanation

The domain of a reciprocal function is all real numbers except for 0. This is because the reciprocal of 0 is undefined. Therefore, the correct choice is 'All real numbers except for 0'.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.5

What is the range of a reciprocal function and how do you find it?

• Only even numbers

• Only prime numbers

• Only negative numbers

• All real numbers except 0

Answer explanation

The range of a reciprocal function is all real numbers except 0. This is because the reciprocal of any non-zero number is a non-zero number. Therefore, the correct choice is 'All real numbers except 0'.

Tags

CCSS.HSF.IF.A.1

If a reciprocal function is given by f(x) = 1/(x-2), what is the equation of the vertical asymptote?

• x = 1

• x = -2

• x = 2

• x = 0

Answer explanation

The equation of the vertical asymptote for the given reciprocal function f(x) = 1/(x-2) is x = 2. As the denominator (x-2) approaches zero, the function approaches infinity. Therefore, x = 2 is the correct choice.

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

If a reciprocal function is given by g(x) = -2/(x+3), what is the equation of the horizontal asymptote?

• y = -3

• y = -2

• y = 0

• y = 1

Answer explanation

The equation of the horizontal asymptote for the given reciprocal function is y = 0. As x approaches positive or negative infinity, the function approaches y = 0.

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

Explain the effect of the parameter 'a' in the function f(x) = a/(x-1) on the graph of the reciprocal function.

• It affects the horizontal shift of the reciprocal function.

• It affects the vertical stretch or compression of the reciprocal function.

• It has no effect on the graph of the reciprocal function.

• It changes the shape of the reciprocal function to a parabola.

Answer explanation

The parameter 'a' in the function f(x) = a/(x-1) affects the vertical stretch or compression of the reciprocal function.

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.BF.B.3

If a reciprocal function is given by h(x) = 3/(x+4) - 2, what are the coordinates of the vertical and horizontal asymptotes?

• The vertical asymptote is x = 0, and the horizontal asymptote is y = -4

• The vertical asymptote is x = 4, and the horizontal asymptote is y = 3

• The vertical asymptote is x = -3, and the horizontal asymptote is y = 2

• The vertical asymptote is x = -4, and the horizontal asymptote is y = -2.

Answer explanation

The vertical asymptote is x = -4, and the horizontal asymptote is y = -2.

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

CCSS.HSA.REI.D.10