Precalculus

Basic Functions

100

The vertex and the x-intercept(s) of the function f(x) = 25 - x^2

Vertex: (0, 25) x-intercepts: (+/-5, 0)

200

The equation of a line in point-slope form that passes through the points (1,2) and (-3,4)

y-2=-1/2 (x-1) 

OR

y+3=-1/2 (x-4)

300

The composition f(g(h((x))) if f(x)=3x²-4, g(x)=2x+1, h(x)=1/x

3(2/x+1)²-4

400

The Domain of f(x) = (x-5)^1/2 in interval notation

[5,oo)

500

Re-write the quadratic function f(x) = x^2 - 2x + 5 in standard/vertex form

f(x)=(x-1)^2+4

Domain & Range

100

The domain of (x+1)^1/2 in interval notation

[-1, inf)

200

The domain of (2x+1) / (x-5)(2x) in interval notation

x can't be zero or 5 but can be everything else

(-oo, 0) U (0,5) U (5, 00)

300

The range of y=5^x-3+1 and the equation(s) of any asymptote(s)

(1, 00) and horizontal asymptote is y=1

400

POINTS LOST...

UH OH...

500

The domain and range of y=2 sin(2x-pi)-3

D: all real numbers

R: [-5,-1]

Polynomials & Rationals

100

The leading term in f(x)=(x+1)³(5x-1)(x-3)⁴

5x⁸

200

Describe the end behavior of the polynomial. 

Given f(x)=-3x⁷+5x⁴-4x³+9

up to the left and down to the right

300

The result of 2x³-6x+1 divided by x-3

2x²+6x+12+ 37/(x-3)

400

FREE POINTS! 

YAYAY!!!

500

The asymptote(s) and the x-coordinate of all holes of the rational function

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

VA: x=-2/3 and x=-3

HA: y=0

Hole: occurs at x=1/2

Trig Identities

100

Simplify: cos²(x) + sin²(x)

1

200

Simplify: sec²x - 1

tan²x

300

Simplify: cos(-x) csc (-x)

- tan(x)

400

Solve: cos (2x), given sin x = -3/5 and "x" is an angle in Quadrant 3.

7/25

500

Evaluate: sin(pi/12) cos(5pi/12) + cos (pi/12) sin(5pi/12)

1

Trig

100

The conversion of 160 degrees to radians

160/x = 180/pi 

x=160pi/180

=8pi/9

200

The amplitude and period of y=2sin(4x)

amplitude=2

frequency=4, so period=2pi/4 = pi/2

300

The value of tan^-1(-1) on the interval (-pi/2, pi/2)

tan^-1(-1) means we need x so that sin x / cos x = -1, which means sine and cosine must be the same value at this angle, but opposite signs (Q4)

tan^-1(-1) = -pi/4

400

From a point on the ground 47 feet from the foot of a tree, the angle of elevation to the top of the tree is 35º. Find the height of the tree to the nearest foot. (Calculator allowed)

33

500

The solution to 2tan(x)sin(x)+2sin(x)=tan(x)+1 on [0,2pi]

3pi/4, 7pi/4, pi/6, 5pi/6