Precalc Test 1

Identify the degree of this polynomial f(x) = -1/2(x^6) - 2x² + 1

Degree : 6

Left side: down

Right side: down

find the domain: f(x) = 3 - √6-2x

x ≤ 3

find the domain: f(x) = -log (3x-4) + 3

x > 4/3

Identify the end behaviors: f(x) = -2x^4 - 3x² + x - 1

x → - ∞, f(x) → - ∞

x → ∞, f(x) → - ∞

find the range: f(x) = 6 -√2x

y ≤ 6

State the domain: f(x) = 3x³ - 2x - 4

all real numbers

state the domain: h(x) = 2x/(x²-2x-8)

x can not be -2, 4

identify any horizontal & vertical asymptotes: f(x)= (x+5)/(x²-x-2)

y = 0

x = 2, -1

state the range: f(x) = (1/x) - 4

y can not be -4

find the roots: f(x) = x² - 8x + 15

x = 5, 3

identify the vertex: f(x) = (x+8)² - 6

(-8, -6)

simplify: 3/(1-(2/x))

3x/(x-2)

rationalize the denom: 3(√3 + 2)

-3√3 + 6

f(x) = x²+ 6x + 13

(x+3)²+4

find and simplify (f+g), (f-g), fg, and f/g: f(x) = 2x+3, g(x) = -x -1

(f+g)(x) = x + 2

(f-g)(x) = 3x+4

(fg)(x) = -2x²-5x-3

(f/g)(x) = (-2x+3)/-x-1

find and simplify (f(g(x)), g(f(x)), and f(g(2)): f(x) = 4x-3, g(x) = 5x²-2

f(g(x)) = 20x²-11

g(f(x)) = 80x²-120x-3

f(g(2)) = 69

find f(g(x)) and g(f(x)) and state if f and g are inverses: f(x) = 3x + 8, g(x) = (x-8)/3

f(x) and g(x) are inverses

find f(g(x)) and g(f(x)) and state if f and g are inverses: f(x) = 2/(x-5), g(x) = (2/x) + 5

f(x) and g(x) are inverses

find an equation for the inverse function and verify: f(x) = 5x-9

y = (x+9)/5

find an equation for the inverse function and verify: f(x) = (2x-3)/(x+1)

y = (x+3)/(2-x)

find and simplify the difference quotient ((f(x+h) - f(x))/h): f(x) = 4x+1

4

find and simplify the difference quotient: f(x) = -2x²

-4x - 2h

find and simplify the difference quotient: f(x) = x²

2x + h

find and simplify the difference quotient: f(x) = -3x²+2x-1

-6x-3h+2

find and simplify the difference quotient: f(x) = 1/x

1/(x²+xh)