Functions

Question 1

What are the first 7 rows of the Pascal’s triangle?

Answer 1

1
11
121
1331
14641
1 5 10 10 5 1
1 6 15 20 15 6 1

Question 2

Describe the most basic forms of hyperbola, truncus, and square root graphs.

Answer 2

Hyperbola: exponential in 1st and 3rd quadrant
Truncus: symmetrical exponential at the same level
Square root: 90 degrees rotated parabola cut in half

Question 3

What are the formulas that can be used to factorize x^3 expressions?

Answer 3

(x+y)^3= (x+y)(x^2-xy+y^2)
(x-y)^3= (x-y)(x^2+xy+y^2)

Question 4

What is the pattern of cubic expansion?

Answer 4

First two always match +/- of original
Third ones always the opposite
Last ones always a +.

Question 5

What is the formula to be used to find the amount of solutions and how do you use it?

Answer 5

b^2-4ac
>0 -> 2 solutions
=0 -> 1 solution
<0 -> no solution

Question 6

What is the intercept form?

Answer 6

(x/a)+(y/b)=1

Question 7

What does the formula m=tanθ calculate?

Answer 7

The angle a line makes with the horizontal.

Question 8

What does the arrangement of simultaneous equation lines represent?

Answer 8

lines cross= 1 solution point
lines parallel, not crossing= no solution
lines overlapping forming 1 line= infinite number of solutions

Question 9

What of the equation shows if lines will be parallel?

Answer 9

Ratio of x and y values- if ratios are the same then the gradients are equal therefore lines parallel

Question 10

How to find value of m (in equation) that causes line to overlap/ be parallel?

Answer 10

use coefficients to form ratio
use cross multiplication to find 2 solutions of m
sub solutions back in to see if solutions are parallel or what.

Question 11

What is the equation that can be used to find the axis of symmetry?

Answer 11

y= -b/2a

Question 12

How to know what’s the point of inflection?

Answer 12

y= a(x+h)^3 +k
point: (-h, k)

Question 13

The square root function exists in _______ only. (original without translation)

Answer 13

Quadrant 1

Question 14

What is an even function?

Answer 14

When f(x)= f(-x)

Question 15

What is a piecewise function?

Answer 15

Ones that has different rules for different parts of the domain.

Question 16

Why is this equation not a function?

Answer 16

Because it failed the vertical line test.

Question 17

What is the graph of an inverse function?

Answer 17

Line of f(x) reflected over line of y=x

Question 18

What is the graph of an inverse function?

Answer 18

Line of f(x) reflected over line of y=x

Question 19

What is the factorised form of quadratic equations?

Answer 19

y = a(x-e)(x-f)

Question 20

expand (x+y)^2

Answer 20

x^2+2xy+y^2

Question 21

What are odd functions?

Answer 21

f(x)= -f(-x)
rotational symmetry about the origin
e.g. y=x^3, y=1/x, y=sinx

Question 22

At what circumstance can DRT be used for horizontal transformations?

Answer 22

When it’s factorized.

Question 23

What to say when something is a function?

Answer 23

• each element in the domain has only one image
• passes the vertical line test

Question 24

What to say when the inverse of something isn’t a function?

Answer 24

• F doesn’t pass the horizontal line test
• therefore can conclude that f^-1 fails the vertical line test
• therefore not a function

Question 25

The student notices that with their translations the point (0. 5/2) is transformed to the point (1. 3/2). This confuses the student because they know that f(0)= 5/2 and f-1(5/2)=0
Explain why the translations do not work as the student expected.

Answer 25

An inverse function is reflected along the line 𝑦 = 𝑥 so that the image of a point
ends up on the other side of the line. therefore (0,5/2)-> (5/2,0)

When the points are translated right 1 and then down 1, they are not being
reflected along the line 𝑦 = 𝑥. therefore (0,5/2)-> (1,5/2)-> (1,3/2)

The point (1, 3/2) lies on both g(x) and f-1
(x)but is not the inverse image from f(x)