Question

Are the statements about the graph of function f true or false?

Answer 1

Answer:

Step-by-step explanation:

1). For a point (0, -15),

   Here x = 0, so the piece of function that applies,

   f(x) = 4x - 15 (Since, x = 0 lies in the range  -2 ≤ x < 4)

         = 4(0) - 15

         = -15

   True.

2). Since, f(x) = $-\frac{1}{4}x^{2}+6x+36$ for x < -2

                     = 4x - 15 for -2 ≤ x < 4

    Which shows a gap between these graphs.

    Therefore, graph has a discontinuity at x = -2

    True.

3). For x > 4,

   f(x) = $3^{x-4}$

   For every input value of x in the interval (4, ∞), output values of the function will be increasing.

  So this option is TRUE.

4). In the interval (-12, -2),

   Function to be followed → f(x) = $-\frac{1}{4}x^{2}+6x+36$

   Graph of the given quadratic function opens downwards (Since, coefficient of x² is negative).

   In this graph value of function first increases then decreases.

   So the answer is FALSE.

5). Since, input values of the function 'f' varies from (-∞, ∞)

   Therefore, domain of the function will be (-∞, ∞)

   TRUE.