Everything Maths Grade 10

4.Given the following equation:

y=

2

x

2

a)Determine the location of they-intercept.

b)Determine the location of thex-intercept.

5.Given the following graph, identify a function that matches each of the following equations:

 4  3  2  1 1 2 3 4

 4

 3

 2

 1

1

2

3

4

h(x)

g(x)

k(x)

f(x)

x

y

a) y=

2

x

b)y=

4

x

c) y=

2

x

d)y=

8

x
6.Given the function:xy= 6.

a)Draw the graph.

b)Does the point(2; 3)lie on the graph? Give a reason for your answer.

c)If thex-value of a point on the graph is 0,25 what is the correspondingy-value?

d)What happens to they-values as thex-values become very large?

e)Give the equation of the asymptotes.

f)With the liney=xas a line of symmetry, what is the point symmetrical to(2; 3)?

7.Given the function:h(x) =

8

x

.

a)Draw the graph.

b)How would the graph ofg(x) =

8

x

+ 3compare with that ofh(x) =

8

x

? Explain your answer fully.

c)Draw the graph ofy=

8

x

+ 3on the same set of axes, showing asymptotes, axes of symmetry and

the coordinates of one point on the graph.

176 6.4. Hyperbolic functions