Question

Need Help PLEASE


Transformations, Graphs, and Diagrams:
1) For the function $g(x)=-2[\frac{1}{0.5(x-3)}] +4$

a) State the following information:
= _____ = _____ = _____ = _____ [2]

b) State any asymptotes. [1]

c) Sketch the transformed function () = −2 ) !
$(\frac{x}{k}+d,ay+c)$, including table of key
points with transformations. In you graph clearly state the points and asymptote(s).
[3]

d) Correctly state the domain and range of the function () sketched above.

Answer 1

The asymptotes of the reciprocal function are x = 3 and y = 4. Also, the domain is x < 3 or x > 3 and the range is y < 4 or y > 4

How to determine the values of a, c, d and k?

The function is given as:

f(x) = -2[1/0.5(x -3)] + 4

A reciprocal function is generally represented as:

f(x) = a[1/(x -c)] + k

So, we have:

a = -2

c = -3 * 0.5

c = -1.5

k = 4

d = 0

Hence, the values of a, c, d and k are -2, -1.5, 0 and 4

The asymptotes

We have:

f(x) = -2[1/0.5(x -3)] + 4

Set the radical to 0

y = 0 + 4

Evaluate

y = 4

Set the denominator to 0

x - 3 = 0

Evaluate

x = 3

Hence, the asymptotes are x = 3 and y = 4

The graph of the function

See attachment for the graph of the function f(x) = -2[1/0.5(x -3)] + 4

The table of values is

x         y

-4        4.6

-2      4.8

2        8

4        0

From the graph of the function, the domain is x < 3 or x > 3 and the range is y < 4 or y > 4

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