Week 4 - Functions

Question 1

When two variables are related, I.E Y depends on the value of X…how do we express this mathematically?

Answer 1

‘Y is a function of X’

Y = f(x)

Question 2

In a function, which is the dependant and independent variable.

Answer 2

Y = f(x)

Y = dependant
X = independant

Question 3

What is the difference between fixed points, arbitrary fixed points and variable points on a graph?

Answer 3

Fixed Points = Points where the coordinates are known

Arbitrary Fixed Points = Points where the coordinates are not known numerically…AKA ‘Subscripts’

Variable points = Points which are not fixed, could take any value

Question 4

What is a linear function?

Answer 4

A function where x is not raised to a power of anything, meaning that on a graph it is a straight line.

f(x) = a + bx

Question 5

How do you plot the graph of a linear function?

Answer 5

Find the intercept = WHen X = 0 … so where line crosses Y axis

Find the root = When Y = o…so where line crosses x axis

Question 6

How do you calculate the gradient of a linear function?

Answer 6

Take two points on the line, make a triangle and then V / H

Question 7

If a linear function takes the form y = a + bx
What is the slope, intercept and root?

Answer 7

Slope = B
Intercept = A
Root = -a/b

Question 8

How will increases in X affect Y in a linear function if:
a) b is positive
b) b is negative
c) b is = 0

Answer 8

a) Y increases
b) Y decreases
c) Changes in x have no effect on Y

Question 9

What are the steps to follow when plotting the graph of a quadratic function?

Answer 9

1st) Find intercept, when x=0
2nd) Find 2 roots, when y=0
3rd) Find Y for selected other values of x