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Licemer1 [7]
3 years ago
12

The graph of y=f(x) is the solid black graph below. Which function represents the dotted graph?

Mathematics
1 answer:
Fed [463]3 years ago
3 0

Answer:   y = f(x - 4) - 1, lower left corner

=============================================================

Explanation:

Let's focus on only the left-most points of each curve

For the black semicircle, the left-most point is located at (-7,0). The corresponding point on the red semicircle is at (-3,-1)

To go from (-7,0) to (-3,-1), we will do two things

  • Shift 4 units to the right
  • Shift 1 unit down

This can be done in any order. The action of "shift 4 units to the right" is effectively the same as shifting the xy axis 4 units to the left while keeping the curves fixed in place. This gives the illusion of movement. When we shift 4 the xy axis 4 units to the left, we're replacing each x input with x-4 as the new input.

In short, we go from f(x) to f(x-4). This is why we have this opposite motion going on.

The up and down motion is fairly straight forward. To shift 1 unit down, we subtract off 1. This is to subtract 1 from the y coordinate.

Overall, we go from y = f(x) to y = f(x - 4) - 1

Applying this transformation will move (-7,0) to (-3,-1) as described above. It will also move every other point on the black curve to their new corresponding location on the red curve.

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Answer:

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Step-by-step explanation:

A linear function f(x) is given with two points, (2,3) and (0,4) lying on the line representing f(x).

It is asked to determine the slope of the line and state if the function is increasing or decreasing. of the value of the slope obtained.

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The points as given in the question are (2,3) and (0,4). Now, the formula for the slope is given as

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So, substitute $4 \& 3$ for $y_{2}$ and $y_{1}$ respectively, and $0 \& 2$ for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows,$m=\frac{4-3}{0-2}$\\ $m=\frac{1}{-2}$\\ $m=-\frac{1}{2}$

The slope of the line is obtained as $-\frac{1}{2}$. Now, as $-\frac{1}{2} < 0$, so the function f(x) is decreasing.

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