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Parent functions

200

y = 4

horizontal line at y = 4.

400

y = x²

concave up parabola

600

y = |x| / x

y = -1 if x < 0

y = 1 if x > 0

800

y = e^x

y --> 0 as x --> -inf

y --> inf as x --> inf

contains the point (0, 1)

1000

y = ln(x)

y --> -inf as x --> 0^-

y --> inf as x --> inf

contains the point (1, 0)

Logs and Exponentials

200

e⁰ + e¹

e + 1

400

ln(0)

Does not exist

600

Solve.

ln(50) - ln(5) + ln(2) = ln(x)

20

800

Solve.

ln(x+5) = ln(x - 1) - ln(x - 1)

No solution

1000

Solve.

2x²e^2x + 2xe^2x = 0

x = -1, 0

Simplifying trig

200

sin(x)sec(x)

tan(x)

400

3(sin(x) + cos(x))² - 6sin(x)cos(x)

3

600

tan(-x)cos(x)

-sin(x)

800

sin(x)tan(x) + cos(x)

sec(x)

1000

(1 - sin²(x)) / (csc²(x) - 1)

sin²(x)

Matrices

200

What are the dimensions of the following matrix?

3  4  6

8  2  1

2x3

400

3  2      +      3  -2

4  -2             2  -1

6  0

6  -3

600

4  -1    *    2  -1

2  -3          0  6

8  -10

4  -20

800

Use your calculator to solve.

3x + 2y - 3z = 4

4x - 3y + 2z = 0

-3x + y - 4z = -5

x = 1

y = 2

z = 1

1000

The following message was encoded with a 2x2 matrix. The last four letters are POND.

1  4  -16  35  7  28  -12  51  3  100  -18  27  14  56  1  4  -7  115  -23  40  12  48  -14  109  6  68

A BIG FISH IN A SMALL POND

Polar/parametric functions

200

Eliminate the parameter to write the rectangular equation represented by the following:

x = t

y = 4t

y = 4x

400

Eliminate the parameter to write the rectangular equation represented by the following:

x = 4cos(t)

y = 2sin(t)

x²/16 + y²/4 = 1

600

Convert from polar coordinates to rectangular coordinates.

(-2, 7π/6)

((sqrt(3)), 1)

800

Convert the equation to rectangular coordinates.

r = 4sin(θ)

x² + y² - 4y = 0

1000

Convert the equation to polar coordinates and give an equation solved for r:

3x - y + 2 = 0

r = -2 / (3cos(θ) - sin(θ))