A6

Question 1

Difference between equation and identity

Answer 1

equation is true for only specific values of the variables

identity is true for all values of the variables

Question 2

How do you do inverse functions +inverse functions on a graph

Answer 2

to do f^-1(x) you need to get f(x)
assume f(x) = 4x
replace f(x) with y to get y = 4x
switch y and x to get x = 4y
solve for y: y = x/4
so f^-1(x) = x/4

a reflection of the original function’s graph across the line y=x

Question 3

When do you use completing the square

Answer 3

When regular factorising doesn’t work

Question 4

How do you complete the square
ie: x^2 + 6x - 2

and what if b is an odd number

Answer 4

ax^2 + bx + c

(x + (1/2 of b))^2 - (1/2 of b)^2
(if b is an odd number just write it as a fraction)

this would be (x+3)^2 - 9

since we still have the -2 we need to rewrite this as (x+3)^2 - 9 - 2 = (x+3)^2 - 11

Question 5

How do we find the turning point via completing the square

Answer 5

Say the answer to completing the square is (x-4)^2 - 13 then you need to solve for x so the answers are either -13 (outside the bracket so it stays the same) or 4 (inside the bracket so needs to equal 0]

the turnign point would be 4,-13

Question 6

How do you solve by completing the square

Answer 6

you take the whole number onto the other side of the equals

Ie: if (x+2)^2 - 6 then you make it (x+2)^2 = 6

So we root both sides to make it + or - 6. WE NEED THE + OR -

then we make the integer/other number to the other side leaving just x (ie: x = -2 + or - 6)

Question 7

If a graph is drawn y = f(x) then what would the effects of the graph be if the function changed to

f(x+3)
f(x)+3

Answer 7

as the change is inside the bracket the graph is being affected on the x axis. Because it is inside, the x does the opposite, so instead of moving the whole graph 3 spaces to the right we make it 3 spaces to the left

As the change is outside the bracket the graph is being affected on the y axis. Because it is outside, the y does what its meant to do, and the graph increases 3 spaces up

Question 8

How do we transform y = -f(x) and y = f(-x) when were given y = f(x)

Answer 8

imagine the x axis is a mirror line and flip the graph that way as the change is outside the bracket so the position of the graph is affected by the y axis

imagine the y axis is a mirror line and flip the graph that way as the change is inside the bracket so the position of the graph is affected by the x axis

Question 9

If a graph is shown y = f(x) then how do we find out the domain and range of that function

Answer 9

Domain: The range of the function shown for the X AXIS. Ie: if the function shown starts and -5 and ends at 5 we write it as -5 < (or equal to) x < (or equal to) 5

Range: The range of the function shown for the Y AXIS. Ie: if the function ranges from y = -2 to y = 3 then we write: -2 < (or equal to) f(x) < (or equal to) 3

Question 10

If you’re being asked a question like

“f(x) = x^2 - 25 for all values of x: Find the range” what to do

Answer 10

Find the turning point of the graph as the y value can go up infinitely (as its for all values of x) but it only has one turning point (5 on the y axis - found by completing the square)

therefore its f(x) > (or equal to) 5

Question 11

What can we deduce from a graph if we have the simple factorised version of it (ie: (x+3) (x+5))

Answer 11

the roots

As one of the solutions to x (roots) has to equal to 0 (y = 0 at the roots), x = -3 or -5 so those r the roots

Question 12

If we have the roots of the quadratic graph how do we find the coordinates of the turning point

Answer 12

As the parabola is symmetrical we find the middle of the 2 roots (ie: if the roots are x = 3 and 5, the middle will be 4). Then we substitute that x value into the equation (ie: (x+3) (x+5)) to find the y value

Question 13

If a question says f(x) = … and it asks to find the range from x values … to … what do you do

Answer 13

Construct the table of x and y substitute each value of x into the equation to get the corresponding y value