Given:
Consider the function is:
To find:
The average rate of change over the interval 2 ≤ x ≤ 4.
Solution:
We have,
At ,
At ,
The average rate of change of a function f(x) over the interval [a,b] is:
So, the average rate of change over the interval 2 ≤ x ≤ 4 is:
On further simplification, we get
Therefore, the average rate of change over the interval 2 ≤ x ≤ 4 is 2.
Answer:
The answer is C
Step-by-step explanation:
Just calculate it
Answer:
Yes because they have the same slope of 3/2
Step-by-step explanation:
The slope of PQ is ...
(10 -7)/(2 -0) = 3/2
The slope of RS is ...
(8 -5)/(0 -(-2)) = 3/2
The slopes are the same (3/2), so the lines are parallel.
Answer:
It is the fourth one.
Step-by-step explanation: You use it to find it to see if it is a right triangle.
Answer:
The +1 in f(x) is the y intercept
The +1 in g(x) is the y coordinate of the vertex
Step-by-step explanation:
For f(x), plugging in x = 0 leads to
f(x) = 2x^2+5x+1
f(0) = 2(0)^2+5(0)+1
f(0) = 1
Showing that (0,1) is the y intercept of f(x).
The same is not true for g(x)
g(x) = 2(x+5)^2+1
g(0) = 2(0+5)^2+1
g(0) = 51
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The +1 for g(x) represents the y coordinate of the vertex. Recall that vertex form in general is
y = a(x-h)^2+k
with (h,k) being the vertex. This means we can quickly spot the vertex for g(x) without having to graph. The same cannot be said for f(x) as we need to complete the square to get f(x) into vertex form. Currently, f(x) is in standard form.