Unit 5 - functions 1

Question 1

How to test if a graph is a function?

Answer 1

Vertical line test - if vertical line passes through graph once, it’s a function

Question 2

Possible vs impossible mapping

Answer 2

Possible - one to one, many to one
Impossible - many to many, one to many

Question 3

Domain vs range

Answer 3

Domain - x axis (where something is horizontally)
Range - y axis (where something is vertically)

Question 4

Solve f(x) = 50-x^2 when f(5)

Answer 4

f(x) = 50-5^2 = 50-25 = 25
f(x) = 25

Question 5

Composite functions - f(x) = 3x-1; g(x) = x^2 +1; get fg(x)

Answer 5

Put the value of g(x) into x in f(x)
f(x) = 3(x^2 +1) - 1 = 3x^2 + 3 -1 = 3x^2 + 2

Question 6

How to do inverse function: f(x) = (5x-2)/3

Answer 6

1. Replace f(x) with y; y = 5x-2/3
2. Replace y with x; x=5y-2/3
3. Make y the subject of the equation; 5y-2 = 3x; 5y = 3x+2; y = (3x+2)/5
   Written as f^-1 = (3x+2)/5

Question 7

What does the absolute value/modulus function give?

Answer 7

Gives the true value (therefore positive) of any number. Represented by 2 straight lines around number.

Question 8

What is an asymptote?

Answer 8

A (usually straight) line that a curve approaches towards infinity but never reaches. Represented by a dotted line.

Question 9

How to find vertical asymptote + y=4/(x+3) - 1

Answer 9

The vertical asymptote is where the function is not defined due to division by 0. We need to work out the value of x that makes the denominator 0.
y=4/(x+3) - 1; x+3 = 0; x = -3

Question 10

How to find the horizontal asymptote + y=4/(x+3) - 1?

Answer 10

Where the graph tends towards positive or negative infinite x. 2 ways to find it:
1. If equation is in the format y = a + b/(cx+d), horizontal asymptote is a because x is made very large, making b/(cx+d) very small and unimportant. So, in y=4/(x+3) - , horizontal asymptote is -1
2. If the equation is in the format (ax^n+b)/(bx^m + c); if n=m, horizontal asymptote is a/b. If n<m, horizontal asymptote is 0, and if n>m, it doesn’t exist.