Consider the graph of the quadratic function. Which interval
1 answer:
Answer:
Option D. 1 to 2.5
Step-by-step explanation:
<u><em>The complete question is</em></u>
Consider the graph of the quadratic function. Which interval on the x-axis has a negative rate of change?
Options:
A. –2 to –1
B. –1.5 to 0
C. 0 to 1
D. 1 to 2.5
see the attached figure to better understand the problem
we know that
The quadratic function in the graph represent a parabola open downward
The vertex represent a maximum
The x-coordinate of the vertex is approximately 0.5
The axis of symmetry is x=0.5
The function is increasing for x < 0.5 interval (-∞,0.5)
The function is decreasing for x > 0.5 interval (0.5,∞)
Remember that
If the function is decreasing, the rate of change is negative
If the function is increasing, the rate of change is positive
so
The rate of change is negative in the interval (0.5,∞)
therefore
Option A. –2 to –1 ----> rate of change is positive
Option B. –1.5 to 0 ----> rate of change is positive
Option C. 0 to 1 ---> (0,0.5) the rate of change is positive and (0.5,1) the rate of change is negative
Option D. 1 to 2.5 ---> <em>the rate of change is negative</em>
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Given the function:
The function can also be written as:
The range of the function will be all set of y values.
To find the range, let's graph the function below.
We have:
From the graph above, all possibe y values range from 0 to infinity.
Therefore, the range of the function is from zero infinity.
In interval notation:
Range = (0, +∞)
ANSWER:
4. (0, +∞)
