9514 1404 393
Answer:
top-down
f(g(x)) = 1, 4, 5, 3, 2
g(f(x)) = 5, 2, 4, 1, 3
Step-by-step explanation:
To find f(g(x)), locate g(x) in the third column (labeled g(x)). Use that value as x in the first column, then read f(x) from the second column.
Example: f(g(1)) = f(2) = 1
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To find g(f(x)), locate f(x) in the second column (labeled f(x)). Use that value as x in the first column, and read the corresponding g(x) from the third column.
Example: g(f(1)) = g(2) = 5
Answer:
Step-by-step explanation:
- The products of corresponding x- and y- values of an inverse variation function are constant.
- As x increases, y also increases.
-The product of the coordinate pairs are not equal: (165)(198)=32,670 and (170)(204)=34,680
"Percent" means literally per one-hundred so
0.12/100
0.0012
Part A: To get an equation into standard form to represent the total amount rented (y) that Marguerite has to pay for renting the truck for x amount of days, we use the formula for the equation of a straight line.
Remember that the equation of a straight line passing through points is ( x_{1} , y_{1} ) and the points ( x_{2} , y_{2} ) is given by
y - y_{1} / x - x_{1} = y - y_{2} / x - x_{2}
Knowing that Marguerite rented a truck at $125 for 2 days, we know if she rents the exact same truck for 5 days, she has to pay a total of $275 for the rent.
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This means that the line modeling this situation crosses points at (2, 125) and (5, 275).
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The equation modeling <span>the total rent (y) that Marguerite has to pay for renting the truck for x days is given by
</span><span>
y - 125 / x - 2 = 275 - 125 / 5 - 2 = 150 / 3 = 50
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But if you are writing the equation in standard form it would be <span>
</span><span>
50x - y = -25
Part B:
When writing the function using function notation it means you are making y the subject of the formula and then replacing the y with f(x).
</span>
If you remember that from part A, we have that the equation for the total rent which is y that Marguerite has to pay for renting the truck for x amount of days is given by
y = 50x + 25.<span>
</span><span>
Writing the equation using the function notation would give us this
f(x) = 50x + 25
Part C:
To graph the function, we name the x-axis the number of days and name the y-axis total rent. The x-axis is numbered using the intervals of 1 while the y-axis is numbered using the intervals of 50.
The points of </span>(2,125) and of (5,275) are marked on the coordinate axis and a straight line is drawn to pass through these two points.
