 Mathematics
Grantham University Week 5 Evaluating Functions Work Sheet Paper

Grantham University

### Question Description

Evaluate the function ƒ(x) = 6x - 5 at ƒ(1)

Find all real values of x such that ƒ(x) = 0 for ƒ(x) = 42 - 6x

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Is the relation a function?
y = x2 + 12x + 31
Question 1 options:
Yes
No

Question 2 (5 points)

Write the standard form of the equation of the circle with radius 7 and center at (0, 0).
Question 2 options:

x2 + y2 = 49
x2 + y2 = 14
x2 + y2 = 7
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Question 3 (5 points)

Convert the equation to the standard form for a hyperbola by completing the square on x and y.
x2 - y2 + 6x - 4y + 4 = 0
Question 3 options:
(x + 3)2 + (y + 2)2 = 1

-

=1

(x + 3)2 - (y + 2)2 = 1
(y + 3)2- (x + 2)2 = 1
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Question 4 (5 points)

Find the location of the center, vertices, and foci for the hyperbola described by the equation.

-

=1

Question 4 options:
Center: ( -4, 1); Vertices: ( -10, -1) and ( 2, -1); Foci: ( -4 Center: ( 4, -1); Vertices: ( -2, -1) and ( 10, -1); Foci:

Center: ( -4, 1); Vertices: ( -9, 1) and ( 3, 1); Foci: ( -3 +
Center: ( -4, 1); Vertices: ( -10, 1) and ( 2, 1); Foci:
(
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Question 5 (5 points)

, -1) and ( -4 +

, -1)

and

, 2) and ( 2 +
and

, 2)

Write the equation in terms of a rotated x'y'-system using θ, the angle of rotation. Write the equation
involving x' and y' in standard form. xy +16 = 0; θ = 45°
Question 5 options:

+

=1

y'2 = -32x'

-

=1

+

=1

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Question 6 (5 points)

Find the standard form of the equation of the ellipse and give the location of its foci.

Question 6 options:

+

=1

foci at (-7, 0) and ( 7, 0)

+

=1

foci at (-

-

, 0) and (

, 0)

, 0) and (

, 0)

, 0) and (

, 0)

=1

foci at (-

+
foci at (-

=1

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Question 7 (5 points)

Match the equation to the graph.
x2 = 7y
Question 7 options:

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Question 8 (5 points)

Convert the equation to the standard form for a hyperbola by completing... vmohanakumar (2581)
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