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1 answer:
The parent function of g(x) = |x - 7| +6 is f(x) = |x|
<h3>How to determine the parent function?</h3>The function is given as:
g(x) = |x - 7| +6
The above function is an absolute function, and the parent function is f(x) = |x|
Hence, the parent function of g(x) = |x - 7| +6 is f(x) = |x|
<h3>The reflection</h3>When f(x) is reflected across the x-axis, we have:
f'(x) = -|x|
When f(x) is reflected across the y-axis, we have:
f'(x) = |x|
<h3>Stretching and Compression</h3>When f(x) is stretched horizontally by a factor k
g'(x) = |kx|
When f(x) is stretched vertically by a factor k
g'(x) = k|x|
<h3>Horizontal Shift</h3>When f(x) is shifted horizontally by k units
f'(x) = |x ± k|
<h3>Vertical Shift</h3>When f(x) is shifted vertical by k units
f'(x) = |x| ± k
See attachment for the graph of g(x)
Read more about function transformation at:
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Answer:
For 124 chirps per minute the temperature is 68 ºF.
For 68 chirps per minute the temperature is 54 ºF.
Step-by-step explanation:
Linear functions are those whose graph is a straight line. A linear function has the following form
b is the constant term or the y intercept. It is the value of the dependent variable when x = 0.
m is the coefficient of the independent variable. It is also known as the slope and gives the rate of change of the dependent variable.
We know that
- At 104 chirps per minute, the temperature is 63 ºF.
- At 176 chirps per minute, the temperature is 81 ºF.
This information can be converted to Cartesian coordinates (x, y). Where x = the number of chirps per minute and y = the temperature in ºF.
To find a linear function that let us find the outside temperature from how fast crickets chirp we must:
- Find the slope:
- Find the equation:
Solving for b
Therefore, the linear function is
Now, using this linear function we can know the temperature when we know the chirps per minute:
For 124 chirps per minute the temperature is:
For 68 chirps per minute the temperature is: