Everything Maths Grade 10

Worked example 24: Interpreting graphs QUESTION The graphs ofy=x^2 + 4andy=x 2 are given. Calculate the following: 1.coordinates ...

Step 2: Calculate the point of intersectionE AtEthe two graphs intersect so we can equate the two expressions: x2 =x^2 + 4 )x^2 ...

SOLUTION Step 1: Examine the sketch From the sketch we see that the graph is a sine graph that has been shifted vertically upwar ...

2.Determine the equations for the graphs given below. a) 5 4 3 2 1 1 2 3 4 5 8 6 4 2 2 4 6 8 (2; 0) (0; 2) x y b) 12 ...

c)The y-intercept of 2 x+ 1is: i. 3 ii. 1 iii. 2 iv. 0 d)Which of the following passes through(1; 7)? i.y=^7 x ii.y= 2x+ 3 iii.y ...

b) x 50 100 150 200 250 300 y 1 2 3 4 5 6 3.Create a table of values from the function given and then plot the function. Your ta ...

7.State whether the following is true or not a)They-intercept ofy+ 5 =xis 5. b)The gradient ofy=x+ 2is 1. c)The gradient of 4 y= ...

6 5 4 3 2 1 1 2 3 4 5 6 5 4 3 2 1 1 2 3 4 5 6 7 B A x y 13.Given the following equation: y= 5 x^2 + 3 a)Calculate the ...

15.Given the following graph, identify a function that matches each of the given equations: 3 2 1 1 2 3 4 2 2 4 6 8 10 12 f ...

18.The following graph shows a hyperbolic equation of the formy= a x +q.Point Ais shown at(1;5). Calculate the values ofaandq. ...

21.Sketch the following functions and identify the asymptotes: a)y= 3 x + 4 b)y= 1 x c)y= 2 x 2 22.Sketch the functions given a ...

26.Given the following graph, identify a function that matches each of the given equations 5 4 3 2 1 1 2 3 4 5 5 4 3 2 ...

30.After a ball is dropped, the rebound height of each bounce decreases. The equationy= 5(0,8)xshows the relationship between th ...

15 30 45 60 75 90 105 120 135 150 165 180 5 4 3 2 1 1 2 3 4 5 A B x y 35.Given the following graph, identify a function tha ...

90 180 270 360 4 3 2 1 1 2 3 4 g(x) =j,8cos f(x) x y What is the equation forf(x)? 37.With the assistance of the table belo ...

b) 90 180 270 360 3 2 1 1 2 3 y= 2cos E x y 41.State the coordinates atEand the domain and range of the function in the inte ...

43.For which values ofis the function increasing, in the interval shown? 90 180 270 360 3 2 1 1 2 3 y= 3sin x y 44.For whic ...

b) 0 (1; 1) (0; 3) x y c) 0 (3;1) x y d) 0 (4;6) (0;2) x y Chapter 6. Functions 227 ...

e) 90 ◦ 180 ◦ 270 ◦ 360 ◦ 4 1 6 x y f) 0 (0; 3) (2; 9) y= 1 x y g) 90 ◦ 180 ◦ 270 ◦ 360 ◦ 2 2 (180◦;2) (135◦;1) x y 228 6.8. C ...

46. 90 180 270 360 3 2 1 1 2 3 f(x) g(x) D C B A x y a)State the coordinates atA; B; CandD. b)How many times in this interval ...