Question

Which of the following can be the parent function of the graph? Select two of the following that apply.

Answer 1

Answer: writing equations of trigonometric functions

1. C-tan x and D- cot x

2. D- f(x) is g(x) compressed vertically by a factor of eight and reflected about the X axis

3. A- -sec x/3 +2 D- sec(x/3+pi)+2 F- csc(x/3+3pi/2) +2

4. C- The equation of the graph should be f(x) sin x/3

Explanation:

Answer 2

Options c and d

Explanation:

Given is a graph with period pi.

ii) The graph is discontinuous

iii) x intercepts are say (a) units to the right of y axis and repeats for every interval of pi.

Fix the function

a) y = sinx cannot be this graph because sinx is a continuous graph

b) y =cosx cannot be this graph because cosx is a continuous graph

e) y = sec x is undefined for the range (-1,1) since the given graph is defined in this interval, secx is not answer.

f)y = csc x is undefined for the range (-1,1) since the given graph is defined in this interval, cscx is not answer.

c) y=tanx is a discontinuous graph at x = odd multiples of pi/2

Hence the given graph can be of the form y =- tan (2x+a) which shows reflection over y axis,

d) y = cotx can also be this graph with adjustments for period and horizontal shift.

So answers are c and d