Algebra and functions review

GDC

100

How do you graph a function?

1. Press "y="

2. Input your function

3. Press "graph"

200

How do you zoom out to view a function?

1. Assume your function is already graphed

2. Press "zoom"

3. Increase your  "x max" and "y max"

4. Decrease your "x min" and "y min"

300

How do you find the roots of x² + 5x + 6

1. Graph the function

2. Press 2nd trace

3. Press 2

4. Go to the left side of one root

5. Click enter

6. Go to the right side of one root

7. Click enter

8. Repeat for the other root

400

How do you find the local maxima of some function f(x)

1. Assume function is drawn

2. Press 2nd trace

3. Move cursor to the left of the local maxima

4. Press enter

5. Move cursor to the right of the local maxima

6. Press enter

500

Bob and Dylan are taking part in their school race. Their distance traveled can be modeled as a function of time. Bob's distance traveled is modeled by f(t) while Dylan's distance can be modeled by g(t) where t is time in minutes.

Given that f(t) = 3t² and g(t) = 5t + 3, find the time at which both Bob and Dylan have traveled the same distance. Solve only using a GDC. Give your answer to 2 d.p

2.13

Basic algebra and quadratics

100

Solve for x:

x + 3 = 3³

x = 24

200

Factorise

x² + 7x + 12 = 0

(x+4)(x+3)

300

Solve the following simultaneous equations:

3x + y = 83

3x - y = 25

x = 18

y = 29

400

Complete the square for 2x² + 10x + 12 = 0

(x+2.5)² - 0.25 = 0

500

Given that R = sin(v²/2at), rearrange the equation for t

t = v²/2asin^-1(R)

Law of indices and sequences

100

Write 2²⁰ x 2³⁰ as 2^a where a is a positive integer 

2⁵⁰

200

p²

_________________            =  p^ab

p^-(8/3)

If a = 1/3, find b

b = 14

300

Rationalise

[8+sqrt(2)]/[7-sqrt(3)]

(56+8sqrt(3)+7sqrt(2)+sqrt(6))/46

400

Given that S₁ = 4, S₀ = 1, S₅ = 1024 and S₂ = 16

Find S_n and S₁₀

S_n = 4ⁿ

S₁₀ = 4¹⁰ = 1048576

500

f(x) = 20x

g(x) = x²

S_n = 3n + 2

Find S_f(g(7)) 

2942

Basic functions, graphs and transformations

100

f(x) = 3x² + 7x + 2

Find f(8)

f(8) = 250

f(8) = 3(8)² + 7(8) + 2 = 192+56+2 = 250

200

Suppose you have some function f(x).

Give the vector that translates the graph of f(x) to f(x+2)

(-2

  0)

300

A quadratic function f(x) has it's vertex at (0, 0).

Find the coordinates of the vertex of f(x+4)+3

(-4, 3)

400

 Some function f(x) is graphed. The maximum point of f(x) is (-5, 4). f(x) also intersects (3, 0) and has two roots. Find:

a. f(x) 

b. The second root of f(x)

a. -(1/16)(x+5)² - 4

b. x = -13 

500

What are the vertical and horizontal asymptotes of 

       7

___________

  (x-4)(x-3)

Horizontal asymptotes:

x = 3

x = 4

Vertical asymptotes:

y = 0

Logarithms, Inverse functions and composite functions

100

Evaluate log₂₀₀₀₀1

0

200

f(x) = 7x

g(x) = 3x-2

Find f(g(x))

7(3x-2) = 21x-14

300

Find the inverse of f^-1(x) given that f(x) = 3x+2

(x-2)/3

400

Why can't you evaluate the following logarithm for all values of b<=0:

log_a(b) 

a to any power 'x' will never give you a number less than or equal to 0. Any logarithm will always evaluate to a number greater than 0.

500

log(f(x)) = 2log(x) + log(3)

g(x) = 2x 

Find f(g(7)) and state whether f(g(x)) has an inverse function

log(f(x)) = log(3x²)

f(x) = 3x²

f(g(x)) = 3(2x)² = 12x²

f(g(7)) = 12(7)² = 12 x 49 = 588

As f(g(x)) is a quadratic, it is not 1:1 and therefore does not have an inverse