🥳 Pre-Calculus Pre-Teaching Review 🥳

Linear Equations and Functions

100

Find the slope of the line between the points (1, 2) and (7, 14).

m = 2

200

If f(x) = x² - 3x, find f(-4).

f(-4) = 28

300

If f(x) = 3x + 4 and g(x) = x² + 1, find f(4) + g(3).

f(4) + g(3) = 26

400

Write the point-slope form of the line with m = 12 and passing (9, 19).

y - 19 = 12(x - 9)

500

Write the point-slope form of the line passing through the points (5, 7) and (1, -1).

y + 1 = 2(x - 1)

or

y - 7 = 2(x - 5)

Composition of Functions

100

If a(x) = 4x + 4 and b(x) = 2x + 1, find a(b(x)).

a(b(x)) = 4(2x + 1) + 4 = 8x + 8

200

If m(x) = 5x² and n(x) = 3x, find m(n(2)).

m(n(2)) = 180

300

If r(x) = 6x - 3 and s(x) = ½x², find (r + s)(x).

(r + s)(x) = ½x² + 6x - 3

400

If h(x) = √x and i(x) = 7x² - 3x + 1, find i(h(9)).

i(h(9)) = 37

500

If w(x) = 10x and y(x) = x² + 2x + 1 and z(x) = x³, find z(y(w(-½))).

z(y(w(-½))) = 46,656

Solving Quadratics

100

Multiply (2x + 1)(3x - ½) by FOILing.

6x² + 2x - ½

200

Factor 2x² - 4x - 126.

3(x + 7)(x - 9)

300

Solve for x² + 2x - 15 by Factoring.

x = -5 and 3

400

Solve for 3x² + 7x + ¼ using the Quadratic Formula.
(Round decimal answers to the nearest thousandth.)

x = -2.297 and -0.036

500

Solve for x² + 10x + 8 = 0 by Completing the Square. (Round decimal answers to the nearest thousandth.)

x = -9.123 and -0.877

Rationals and Division of Polynomials

100

Simplify (x² - 6x - 16)/(x² + 3x + 2) by "FOCO"... Factor Out, Cancel Out.

(x - 8)/(x + 1)

200

Use Synthetic Division or Long Division to calculate (x² - 5x + 9) ÷ (x + 3).

x - 8 + 33/x+3

300

Use Synthetic Division or Long Division to calculate (x⁴ - 3x³ + 1) ÷ (x - 5).

x³ + 2x² + 10x + 50 + 251/x-5

400

Find the horizontal asymptote in the rational function (3x⁴ + 1)/(4x⁴).

Horizontal Asymptote at y = ¾

500

Find any hole(s) in the rational function (x² - 7x + 10)/(x² - 25).

Hole at x = 5

Transformations and the Unit Circle

100

Using the Unit Circle, find the value of tan(3π/4).

tan(3π/4) = -1

200

Using the Unit Circle, find sin(-120º) + cos(11π/6).

sin(-120º) + cos(11π/6) = -√3/2 + √3/2) = 0

300

Find the parent function of f(x) = -¾(x⁵ - 2) + 3.

Parent Function is f(x) = x⁵

400

List the transformations for f(x) = -6x² + 3 from its parent function f(x) = x².

-Reflection across the x-axis.
-Translation 3 units up.
-Dilation (stretch) vertically by a scale factor of 6.

500

List the transformations for f(x) = -½|3x - 1| + 5 from its parent function f(x) = |x|.

-Reflection across the x-axis.
-Dilation (compress) vertically by ½.
-Dilation (compress) horizontally by 3.
-Translation 1 unit to the right.
-Translation 5 units up.