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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 containing the point (0, 0), 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) = 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 a periodic function which has a maximum value of 1 and a minimum value of negative 1. It starts at the point (0, 0)
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 a periodic function which has a maximum value of 1 and a minimum value of negative 1. It starts at the point (45 degrees, 1).
A. f(x) = sin(x - 45°)
B. f(x) = sin(x + 45°)
C. f(x) = sin x + 2
D. f(x) = 2sin x
 
asked Sep 27, 2014 in TRIGONOMETRY by tonymate Pupil

3 Answers

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Best answer

1)

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.

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

In this case a full period occur between x =  - π/2 and x = π/2.

  • 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, . . . . .

Amplitude of the graph (maximum y value )

In this case there is no amplitude, since there is no maximum value of y.

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

Option C is correct.

answered Sep 27, 2014 by david Expert
selected Sep 28, 2014 by tonymate
0 votes

2) Observe the graph,this is sine function graph and its contains all properties of the sine 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 odd function, as the symmetry of the graph
    with respect to the origin indicates.
  • The sine 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 . . . , - 2π, - π, 0, π, 2π, . . . ; the y-intercept is 0.
  • Amplitude of the graph (maximum y value )

    In this case amplitude is 1.

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

Option B is correct.

 

answered Sep 27, 2014 by david Expert
0 votes

3)Observe the graph,

  • Amplitude of the graph (maximum y value )

    In this case amplitude is 1.

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

Period of the graph is .

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 . . . , - 9π/4, - 5π/4, -π/4, 3π/4,7π/4. . . .

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, . . . .

In this case

The absolute maximum is 1 and occurs at x = . . . . , - 7π/4, π/4,9π/4 . . . . ;

The absolute minimum is - 1 and occurs at x = . . . , - 3π/4, 5π/4, . . . .

From the above conclusion, The graph shifts to the left by π/4 units.

 

Therfore, the function is f(x) = sin(x + π/4)

f(x) = sin(x + 45°)

Option B is correct choice.

answered Sep 27, 2014 by david Expert

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