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What is the equation of the following graph?

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What is the equation of the following graph?
Graph of a periodic function which has a maximum value of 1 and a minimum value of negative 1. It starts at the point (0, 1)
A. f(x) = cos x
B. f(x) = sin x
C. f(x) = tan x
D. f(x) = cot x
What is the equation of the following graph?
Graph of periodic function with maximum value of one and minimum value of negative one. The graph starts at the point 45 degrees and 1.
A. f(x) = sin(x - 45°)
B. f(x) = sin(x + 45°)
C. f(x) = sin x + 2
D. f(x) = 2sin x
 
What is the equation of the following graph?
Graph of a periodic function containing the point (0, negative 2), extending up to the right as it approaches an asymptote at pi divided by 2. Also extending from the point down to the left as it approaches as asymptote at negative pi divided by 2.
A. f(x) = tan x - 2
B. f(x) = tan x + 2
C. f(x) = 2tan x
D. f(x) = tan x - 3

 

asked Sep 28, 2014 in TRIGONOMETRY by tonymate Pupil

3 Answers

0 votes

1)

Observe the graph,this is cosine function graph and its contains all properties of the cosine function.

  • The domain is all real numbers .
  • Range is [-1, 1]

All real numbers between including between -1 and 1 including -1 and 1.

  • The sine function is an even function, as the symmetry of the graph
    with respect to the origin indicates.
  • The cosine function is periodic,with period 2π.

(Period is length of smallest domain interval which corresponds to a complete cycle of values of the function.)

  • The x-intercepts are . . . , - 5π/2, - 3π/2, -π/2, π/2, 3π/2, 5π/2 . . . ; the y-intercept is 0.
  • Amplitude of the graph (maximum y value )

    In this case amplitude is 1.

Therfore, the function is f(x) = cos(x)

Option A is correct.

answered Sep 28, 2014 by bradely Mentor
0 votes

2)

Observe the graph, this is sine function graph.

The x-intercepts of the y = sinx are . . . , - 2π, - π, 0, π, 2π, . . . ; the y-intercept is 0.

From the graph, the x-intercepts are . . . , - 7π/4, - 3π/4, π/4, 5π, . . . .

From the sin function properties,

the absolute maximum is 1 and occurs at x = . . . . . , - 3π/2, π/2, 5π/2, 9π/2, . . . . ;

the absolute minimum is - 1 and occurs at x = . . . . , - π/2, 3π/2, 7π/2, 11π/2, . . . .

From the graph,

the absolute maximum is 1 and occurs at x = . . . . , - 5π/4, 3π/4, . . . . ;

the absolute minimum is - 1 and occurs at x = . . . , - 9π/4, - π/4, 7π/4, . . . .

From the above conclusion, there is an horizontal shifts π/4 units to right in the graph of y = sin(x). So, the option A is correct.

The option A is correct.

answered Sep 28, 2014 by bradely Mentor
0 votes

Observe the graph, this is tangent function graph and its contains all properties of the Tangent Function.

  • The domain is the set of all real numbers,except odd multiples of π/2.
  • The range is the set of all real numbers.
  • The tangent function is an odd function, as the symmetry of the graph
    with respect to the origin indicates.
  • The tangent function is periodic,with period π.
  • The x-intercepts are . . . , - 2π, - π, 0, π, 2π, . . . ; the y-intercept is 0.
  • Vertical asymptotes occur at x = . . . , - 3π/2, - π/2, π/2, 3π/2, . . . . .

From the graph, the y-intercept is - 2, so there is an vertical shifts 2 units down wards in the graph of y = tan(x). So, the option A is correct.

The option A is correct.

answered Sep 28, 2014 by bradely Mentor

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