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zebragal
26.11.2020 •
Mathematics
Are the statements about the graph of function f true or false?
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Ответ:
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) =
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}](/tpl/images/0930/1962/d040a.png)
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](/tpl/images/0930/1962/3cf08.png)
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.
Ответ:
answer:
f(x) = 100/(2ˣ)
step-by-step explanation:
looking at the graph, i got the points
(0, 100)
(1, 50)
(2, 25)
(3, 12.5)
it seems that the functions is exponentially decaying by half for every x-value increase.
so, my function must have the graph start at 100 and decay by 1/2 every time giving me the equation:
f(x) = 100 * (1/2)ˣ
f(x) = 100 * (1ˣ/2ˣ)
f(x) = 100 * (1/2ˣ) , 1ˣ will always be equal to 1
f(x) = 100/(2ˣ)