GDC
How do you graph a function?
1. Press "y="
2. Input your function
3. Press "graph"
Solve for x:
x + 3 = 33
x = 24
Write 220 x 230 as 2a where a is a positive integer
250
f(x) = 3x2 + 7x + 2
Find f(8)
f(8) = 250
f(8) = 3(8)2 + 7(8) + 2 = 192+56+2 = 250
Evaluate log200001
0
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"
Factorise
x2 + 7x + 12 = 0
(x+4)(x+3)
p2
_________________ = pab
p-(8/3)
If a = 1/3, find b
b = 14
Suppose you have some function f(x).
Give the vector that translates the graph of f(x) to f(x+2)
(-2
0)
f(x) = 7x
g(x) = 3x-2
Find f(g(x))
7(3x-2) = 21x-14
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
Solve the following simultaneous equations:
3x + y = 83
3x - y = 25
x = 18
y = 29
Rationalise
[8+sqrt(2)]/[7-sqrt(3)]
(56+8sqrt(3)+7sqrt(2)+sqrt(6))/46
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)
Find the inverse of f-1(x) given that f(x) = 3x+2
(x-2)/3
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
Complete the square for 2x2 + 10x + 12 = 0
(x+2.5)2 - 0.25 = 0
Given that S1 = 4, S0 = 1, S5 = 1024 and S2 = 16
Find Sn and S10
Sn = 4n
S10 = 410 = 1048576
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
Why can't you evaluate the following logarithm for all values of b<=0:
loga(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.
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
Given that R = sin(v2/2at), rearrange the equation for t
t = v2/2asin-1(R)
f(x) = 20x
g(x) = x2
Sn = 3n + 2
Find Sf(g(7))
2942
What are the vertical and horizontal asymptotes of
7
___________
(x-4)(x-3)
Horizontal asymptotes:
x = 3
x = 4
Vertical asymptotes:
y = 0
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