1Acomplete the Table for Each of These Functions

Cambridge Essentials MathematicsExtension 9A4.2Homework

/ A4.2 Homework

1aComplete the table for each of these functions.

x / –3 / –2 / –1 / 0 / 1 / 2 / 3
y

iy = 2x+3iiy = 8–xiiiy = 2(x–3)

bUse sensible verticaland horizontal scales for the x and yvalues based on values in the table.

Draw a graph of each function.

cWrite down the coordinates of the point where each line cuts the y-axis.

2iFor each of these equations,find the coordinates of two points.

Use the ‘cover up’method.

iiUse the points to draw a separate graph for each equation.

ax + 2y= 4by–3x = 6

c3y – x = 9d3x + 4y – 24 = 0

3aWithout drawing the graphs, write down the gradient and y-intercept of each function.

iy = 3x + 5iiy = 8 – 2xiiiy = x + 6

ivy = 2x – 7vy = x + 1viy= –0.4x + 8

bRearrange each equation into the form y=mx+c.

Then write down the gradient and y-intercept.

i2y = 4x + 5ii3y = x + 6iiiy–2x = 3

vi8x = 3yv4xy = 2viy–3x–1 = 0

4Rearrange the equations and identify the equations parallel lines.

ay=2x–5b3y=2x+4c2y=4x–5

d3y=x+4e5–3y+x=0f6y–4x–5=0

5iFor each straight line, work out the gradient and y-intercept.

iiWrite the equation of the line in the form y=mx+c.

e f

6Find the coordinates of the midpoint of each line.

7Find the coordinates of the midpoint of the line between each pair of points.

a(4,1) and (6,3)b(0,5) and (6, –3)

c(6, –2) and (1,3)d(7,0.5) and (2,2)

8Write down the gradient of the lines perpendicular to the lines with these gradients.

a3b–2cde

9aWrite the gradient of the lines perpendicular to y=x– 1.

bFind the equations of the lines perpendicular to y=x– 1.

The equation for each line should pass through these points.

i(0,0)ii(0,5)iii(0,–7)

10Find the inverse of each function.

ay = 2xby = cy = x+3dy = x–4

ey = 2x+5fy = 3x–2gy = 3x+1hy = 4x–3

iy = 8–xjx+y = 10k4x+5y = 7l3x+6y–12 = 0

11aComplete this table of values for each quadratic function.

bDraw a graph for each function.

x / –3 / –2 / –1 / 0 / 1 / 2 / 3
y

iy=x2iiy=6–x2iiiy=x2+x–6

cFor each of the functions, write down the minimum or maximum value of the curve.

12Without drawing a graph of the function write down the minimum or maximum values of these equations. State whether this value is a minimum or a maximum.

ay=2x2–3by=9–2x2cy=8+x2dy=5–4x2

13aComplete the table of values for each cubic function.

bDraw a graph of each function.

cWrite the coordinates of the pointswhere each graph crosses the y-axis.

x / –3 / –2 / –1 / 0 / 1 / 2 / 3
y

iy=x3+2iiy=8–x3iiiy=x3–10