Consider firing a pumpkin from a canon at a target that is 17 meters away. The pumpkin follows a quadratic path as displayed to
the right. Will the pumpkin hit the target? 1a. Use the graphing calculator to make a table of the given ordered pairs. Include (0,0) in your table. b. Find the equation for the parabola. Round all co-efficients to the nearest tenth. (2 points) c. Find the roots of the equation from part b. (2 points) d. Will the pumpkin hit the target? (1 point)
1 answer:
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Answer:
Step-by-step explanation:
To find the inverse function, solve for y:
f(x) is an even function, so f(-x) = f(x). Then the inverse relation is double-valued: for any given y, there can be either of two x-values that will give that result.
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A function is single-valued. That means any given domain value maps to exactly one range value. The test of this is the "vertical line test." If a vertical line intersects the graph in more than one point, then that x-value maps to more than one y-value.
The horizontal line test is similar. It is used to determine whether a function has an inverse function. If a horizontal line intersects the graph in more than one place, the inverse relation is not a function.
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Since the inverse relation for the given f(x) maps every x to two y-values, it is not a function. You can also tell this by the fact that f(x) is an even function, so does not pass the horizontal line test. When f(x) doesn't pass the horizontal line test, f^-1(x) cannot pass the vertical line test.
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The attached graph shows the inverse relation (called f₁(x)). It also shows a vertical line intersecting that graph in more than one place.
The equivalent expression to the value given using the laws of indices is
Evaluating the options given based on the laws of indices :
Therefore, the only expression which would give a correct way of representing
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