An aquarium measures 11 feet wide, 10 feet long and 7 feet deep. Approximately how many gallons of water does it hold if there a
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The y-intercept of linear function (f- g)(x) is (0,9)
<h3>How to determine the y-intercept?</h3>The table of values is given as:
x -6 -4 -1 3 4
f(x) 15 11 5 -3 -5
g(x) -36 -26 -11 9 14
The equations of the functions is calculated using:
So, we have:
Evaluate
f(x) = -2x + 3
Also, we have:
Evaluate
g(x) = 5x - 6
Next, we calculate (f - g)(x) using:
(f - g)(x) = f(x) - g(x)
This gives
(f - g)(x) = -2x + 3 - 5x + 6
Substitute 0 for x
(f - g)(0) = -2(0) + 3 - 5(0) + 6
Evaluate
(f - g)(0) = 9
Hence, the y-intercept of (f- g)(x) is (0,9)
Read more about linear functions at:
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<h3><u>Explanation</u></h3>
A function is a set of relation that doesn't have repetitive domain. If we want to know if a graph is function or not, we have to do the line test.
<u>Line</u><u> </u><u>Test</u>
- Draw a vertical line. Make sure that a line passes through a graph.
- See if a line intercepts a graph more than one point or just only one.
<u>Result</u>
If a line intercepts a graph more than one point, it is not a function.
However, if a line only intercepts a graph just one point, it is indeed a function.
The given graph from the question is a function because it passes line test.
<u>Domain</u><u> </u><u>and</u><u> </u><u>Range</u>
Domain is the set of all x-values, meaning we only focus on x-axis or x-value only.
Range is the set of all y-values. We only focus on y-value or y-axis for Range.
<u>Determine</u><u> </u><u>Domain</u><u> </u><u>from</u><u> </u><u>Graph</u>
We can simply say that the domain is from starting domain or x-coordinate point to end x-coordinate point. For example, if a graph starts at x = -4 and ends at x = 2, we can say that - 4<=x=2.
<u>Determine</u><u> </u><u>Range</u><u> </u><u>from</u><u> </u><u>Graph</u>
Similar to Domain except Range starts from the minimum value or point to the maximum point or value. For example if a graph starts at min point = 6 and max point = 9. We can say that 6<=y<=9.
From the graph, the domain starts from negative infinity to positive infinity. Meaning that x can be any numbers. Hence, the domain is set of all real numbers. For range, the minimum value is 0 and max value is positive infinity. Therefore we write y>=0.
<h3><u>Answer</u></h3><u></u>
<u>Domain</u><u> </u><u>is</u><u> </u><u>set</u><u> </u><u>of</u><u> </u><u>all</u><u> </u><u>real</u><u> </u><u>numbers</u><u>.</u>
<u>Range</u><u> </u><u>is</u><u> </u><u>greater</u><u> </u><u>or</u><u> </u><u>equal</u><u> </u><u>to</u><u> </u><u>0</u><u>.</u>