College Algebra Ch 3 Review

Decide which equation(s) repesent y as a function of x.
I. 3x − 4y = 12
II. y² = x² − 9
III. y = √(x + 3)
IV. x² + y² − 6y + 8y = 0

• (I) 
• (I) and (III)
• (I), (II), and (IV)
• (I), (III), and (IV)

Tags

CCSS.8.F.A.1

Decide which set(s) represent a function from A to B.
A = {1, 2, 3}    and B = {−3, −4, −7}
(I). {(1, −3), (1, −4), (1, −7)}
(II). {(1, −7), (2, −7), (3, −7)}
(III). {(1, −3), (2, −4), (3, −7)}
(IV). {(1, −4), (2, −4), (3, −3)}

• (I) and (II)
• (II) and (III)
• (III)
• (II), (III), and (IV)

Tags

CCSS.8.F.A.1

Find the domain of the function.
f(t) = √(t − 3) ÷ (t − 5)

• [3, 5) ⋃ (5, ∞)
• (−∞, 3] ⋃ (5, ∞)
• (−∞, −5) ⋃ (−3, ∞)
• (5, ∞)

A person deposits $5000 in an account that pays 6% interest compounded quarterly. Write the balance of the account in terms of the time (t) that the principal is left in the account.

• A(t) = 5000(1.06)t
• A(t) = 5000(0.06)t
• A(t) = 5000(1+.06/4)^4t
• A(t) = 5000(1.06)^t

Determine the domain and range of the function.
f(x) = x² + 1

• Domain: All real numbers; Range: All real numbers
• Domain: All real numbers; Range: [1, ∞)
• Domain: [1, ∞); Range: All real numbers
• Domain: [0, ∞); Range: [−1, ∞)

Determine the domain and range of the function.
f(x) = √(x² − 9)

• Domain: [3, ∞); Range: [0, ∞)
• Domain: (−∞, −3] ⋃ [3, ∞); Range: [0, ∞)
• Domain: [−3, 3]; Range: (−∞, ∞)
• Domain: [−3, 3]; Range: (0, ∞)

Determine if this equation can represent y as a function of x.
x² = 2xy − 1

• Yes.
• No.
• Sometimes, but not always.
• The Vertical Line Test is a little too Undefined for me.

Determine if this equation can represent y as a function of x.
x² + y² = 25

• Yes.
• No.
• Sometimes, but not always.
• Circles have an infinite number of sides, so they are a little too circular for me. I only trust squares.

Use your knowledge of f(x) = x², to determine the shift(s) and/or reflections of the following function.
g(x) = −(x − 1)² − 2

• Reflection across the x-axis, horizontal shift 1 unit right, vertical shift 2 units down
• Reflection across the y-axis, horizontal shift 1 unit left, vertical shift up 2 units
• Reflection across the x-axis, horizontal shift 2 units right, vertical shift 1 unit down
• Reflection across the y-axis, horizontal shift 1 unit left, vertical shift down 2 units

Determine (f − g)(x).
f(x) = x + 2
g(x) = x − 3

• 5
• 2x + 5
• x − 1
• x² − x − 6

Tags

CCSS.HSF-BF.A.1B