Please help with this
1 answer:
Answer:
(a) Horizontal line test
Step-by-step explanation:
A relation that is a function already passes the vertical line test. If it has an inverse function, that function must also pass the vertical line test.
<h3>Inverse relation</h3>The inverse relation will be the same graph reflected across the line y=x. That is, points that are horizontally aligned on the relation graph become vertically aligned on the inverse relation graph.
<h3>Inverse function</h3>If the inverse relation is to be a function, then there must be no points on its graph that are vertically aligned. This requirement translates to the requirement that there be no horizontally-aligned points on the graph of the original relation. The "horizontal line test" checks for horizontally aligned points. If there are none, the test is said to <em>pass</em>.
A function will have an inverse function if it passes the Horizontal Line Test.
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<em>Additional comment</em>
The attached graph shows a function (red curve) that <em>does not pass the horizontal line test</em>. Its inverse relation is the green curve, which you can see is <em>not a function</em>. It does not pass the vertical line test.
The line y=x is shown (dashed orange) so you can see the symmetry of the function and its inverse.
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Answer:
111 spots
Step-by-step explanation:
Let y denote the total number of parking spots expressed as:
Given that x is the number of spots in the first row.
-Now, given that the first row has 32 spots, we substitute in the expression to solve for y:
Hence, there are 111 spots in the parking lot.
Answer:
The equation of the line tangent to the graph of f at x = -1 is .
Step-by-step explanation:
From Analytical Geometry we know that the tangent line is a first order polynomial, whose form is defined by:
(1)
Where:
- Independent variable, dimensionless.
- Dependent variable, dimensionless.
- Slope, dimensionless.
- Intercept, dimensionless.
The slope of the tangent line at is:
(2)
If we know that ,
and
, then the intercept of the equation of the line is:
The equation of the line tangent to the graph of f at x = -1 is .