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Answer:
a. f (x) < 0 for x ∈ (-∞ ,-3)
b. f (x) > 0 for x ∈ (-3,-2)
c. f (x) < 0 for x ∈ (-2,2)
d. f (x) > 0 for x ∈ (2,3)
e.f (x) < 0 for x ∈ (3,∞)
Step-by-step explanation:
Here, the given function is:
Now, to check for the sign of f(x) at x = k, put the value of x from the given interval.
We get:
<u>a. (-infinity, -3) </u>
put k = -4 from the given interval
We get
⇒ f (x) < 0 for x ∈ (-∞ ,-3)
b. (-3, -2)
put k = -2.5 from the given interval
We get
⇒ f (x) > 0 for x ∈ (-3,-2)
c. (-2, 2)
put k = 0 from the given interval
We get
⇒ f (x) < 0 for x ∈ (-2,2)
d. (2, 3)
put k =2.5 from the given interval
We get
⇒ f (x) > 0 for x ∈ (2,3)
e. (infinity, 3)
put k = 4 from the given interval
We get
⇒ f (x) < 0 for x ∈ (3,∞)
Answer:
The equation to represent g(x) will be
Step-by-step explanation:
Considering the logarithmic function
As we know that when a constant c gets added to the parent function, the result would be a vertical shift c units in the direction of the sign of c.
So,
is basically the shift up by 4 units, and the graph also showing the same situation.
Therefore, the equation to represent g(x) will be
Also, the graphs of both and
is attached where black mark graph represents
and red mark graph represents
.
Keywords: transformation, vertical shift, graph
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