Answer :
Answer:
a. (-∞, ∞)
b. (-∞, 4]
c. (-4,0) and (4,0)
d. (0, 1)
e. x = -∞ to x = 2, x = 0 to x = 3
f. x = x = 2 to x = 0, x = 3 to x = ∞
g. relative maximum at points (-2, 4) and (3, 2)
h. relative maximum of f is 4. There is an other relative maximum at xf = 2
f.
Step-by-step explanation:
a) domain is [tex][-4\leq x\leq 4][/tex], b) range is [tex][-\infty < y\leq 4][/tex], c) x intercepts at -4 and +4, d) y intercept at 1, e) f is increasing in [tex][\infty \leq y\leq 4][/tex] and [tex][1\leq y\leq 2][/tex], f) f is decreasing in [tex][4\leq y\leq 1][/tex] and [tex][2\leq y\leq \infty][/tex], h) f has relative maximum at one point, i) f has a relative maxima at [tex]x = -2[/tex].
What is graph of a function?
A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).
For the given situation,
The graph shows the function y = f(x)
a) The domain of f:
The domain is the set of all possible input x values.
Here the function has the input domain between [tex][-4\leq x\leq 4][/tex]
b) The range of f:
The range is the set of all possible output y values.
Here the function has the output range between [tex][-\infty < y\leq 4][/tex]
c) The x intercepts:
The point where the function crosses the x axis.
Here the x intercept is at -4 and +4.
d) The y intercept:
The point where the function crosses the y axis.
Here the y intercept is at 1.
e) Intervals on which f is increasing:
Here the function is increasing at two places
Interval 1 is [tex][\infty \leq y\leq 4][/tex]
Interval 2 is [tex][1\leq y\leq 2][/tex]
f) Intervals on which f is decreasing:
Here the function is decreasing at two places.
Interval 1 is [tex][4\leq y\leq 1][/tex]
Interval 2 is [tex][2\leq y\leq \infty][/tex]
h) The numbers at which f has relative maximum:
It is a point on a function whose y coordinate is larger than all other y coordinates on the graph.
Here the function has relative maximum at one point.
i) The relative maxima of f:
The function f has a relative maxima at [tex]x = -2[/tex].
Hence we can conclude that a) domain is [tex][-4\leq x\leq 4][/tex], b)range is [tex][-\infty < y\leq 4][/tex], c) x intercepts at -4 and +4, d) y intercept at 1, e) f is increasing in [tex][\infty \leq y\leq 4][/tex] and [tex][1\leq y\leq 2][/tex], f) f is decreasing in [tex][4\leq y\leq 1][/tex] and [tex][2\leq y\leq \infty][/tex], h) f has relative maximum at one point, i) f has a relative maxima at [tex]x = -2[/tex].
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