June 2022 Regents Algebra

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The graph of f(x)= x² was transformed to create the graph of g(x) = (x - 7)². Which of these describes the transformation?

• A horizontal shift to the right 7 units

• A horizontal shift to the left 7 units

• A vertical shift down 7 units

• A vertical shift up 7 units

A high school club is researching a tour package offered by the Island Kayak Company. The Company charges $35 per person and $245 for the tour guide. Which function represents the total cost, C (x), of this kayak tour package for x club members?

• C(x) = 35x

• C(x) = 35x + 245

• C(x) = 35(x + 245)

• C(x) = 35 + (x +245)

The expression 3(x + 4) - (2x + 7) is equivalent to

• x + 5

• x - 10

• x - 3

• x + 11

A function is defined as K(x) = 2x² - 5x + 3. The value of K(-3) is

• 54

• 36

• 0

• -18

The solution to 3(x - 8) + 4x = 8x + 4 is

• 12

• 28

• -12

• -28

An ice cream shop sells ice cream cones, c, and milkshakes, m. Each ice cream cone costs $1.50 and each milkshake costs $2.00. Donna has $19.00 to spend on ice cream cones and milkshakes. If she must buy 5 ice cream cones, which inequality could be used to determine the maximum number of milkshakes she can buy?

• 1.50(5) + 2.00(m) > 19.00

• 1.50(5) + 2.00m < 19.00

• 1.50c + 2.00(5) > 19.00

• 1.50c + 2.00(5) < 19.00

When written in standard form, the product of (3 + x) and (2x - 5) is

• 3x - 2

• 2x² + x - 15

• 2x² - 11x - 15

• 6x - 15 + 2x² - 5x

If x = 2, y = 3√2, and w = 2√8, which expression results in a rational number?

• x + y

• y - w

• (w)(y)

• y/x

If the parent function of f(x) is p(x) = x², then the graph of the function

f(x) = (x - k)² + 5, where k > 0, would be a shift of

• k units to the left and a move of 5 units up

• k units to the left and a move of 5 units down

• k units to the right and a move of 5 units up

• k units to the right and a move of 5 units down