Everything Maths Grade 10

Exercise 6 – 4: 1.The following graph shows a hyperbolic equation of the formy= a x +q.Point Ais shown at ( 2; 5 2 ) . Calculate ...

4.Given the following equation: y= 2 x 2 a)Determine the location of they-intercept. b)Determine the location of thex-intercept ...

8.Sketch the functions given and describe the transformation performed on the first function to obtain the second function. Show ...

Complete the following table for each of the functions and draw the graphs on the same system of axes: F(x) = ( 1 2 )x ,G(x) = ( ...

1.We notice that all graphs pass through the point(0; 1). Any number with exponent 0 is equal to 1. 2.The graphs do not cut thex ...

On the same set of axes, plot the following graphs (b= 2,a= 1andqchanges): 1.y 5 = 2x 2 2.y 6 = 2x 1 3.y 7 = 2x 4.y 8 = 2x+ 1 5. ...

0 < b < 1 a < 0 a > 0 q > 0 q < 0 Table 6.5:The effect ofaandqon an exponential graph when 0 <b< 1. Disc ...

Worked example 13: Domain and range of an exponential function QUESTION Find the domain and range ofg(x) = 5: 2 x+ 1 SOLUTION St ...

Asymptotes Exponential functions of the formy=abx+qhave a single horizontal asymptote, the linex=q. Sketching graphs of the form ...

Step 3: Determine the asymptote The horizontal asymptote is the liney= 2. Step 4: Plot the points and sketch the graph 4 3 2 ...

Step 3: Determine the asymptote The horizontal asymptote is the liney= 6. Step 4: Plot the points and sketch the graph 4 3 2 ...

3.Below you see a graph of an exponential function with the equationy=a : 2 x+q. One point is given on the curve:Point Ais at(3; ...

6.Given the functionsy= 2xandy= ( 1 2 )x . a)Draw the graphs on the same set of axes. b)Is thex-axis an asymptote or an axis of ...

Choose an appropriate scale and plot the values ofon thex-axis and ofsinon they-axis. Round answers to 2 decimal places.  0 ° ...

Functions of the formy=asin+q EMA55 Investigation: The effects ofaandqon a sine graph In the equation,y=asin+q,aandqare consta ...

Effect ofa a > 1 : vertical stretch, amplitude increases  y a= 1 a> 1 0 <a< 1 1 <a< 0 a< 1 a= 1: basic si ...

Period The period ofy=asin+qis 360 °. This means that one sine wave is completed in 360 °. Intercepts They-intercept off() =as ...

Cosine function EMA57 Functions of the formy=cos EMA58 Worked example 18: Plotting a cosine graph QUESTION y=f() =cos [0° ...

Functions of the formy=acos+q EMA59 Investigation: The effects ofaandqon a cosine graph In the equation,y=acos+q,aandqare cons ...

Effect ofa a > 1 : vertical stretch, amplitude increases  y a= 0 a> 1 0 <a< 1 1 <a< 0 a< 1 a= 1: basic co ...