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1 answer:
The transformation of a function may involve any change. The function with the graph are given below.
<h3>How does the transformation of a function happen?</h3>The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
- Left shift by c units: y=f(x+c) (same output, but c units earlier)
- Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
- Up by d units: y = f(x) + d
- Down by d units: y = f(x) - d
Stretching:
- Vertical stretch by a factor k: y = k \times f(x)
- Horizontal stretch by a factor k: y = f\left(\dfrac{x}{k}\right)
The real graph of the function is f(x)=x², now if the graph of the given function can be found by using the transformation rule as shown above. The function with the graph are given below.
Learn more about Transforming functions:
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Answer:
Step-by-step explanation:
By definition, two lines are perpendicular if and only if their slopes are negative reciprocals of each other: , or equivalently,
.
Given our linear equation 3x + y = 3 (or y = -3x + 3):
We can find the equation of the line (with a y-intercept of 5) that is perpendicular to y = -3x + 3 by determining the negative reciprocal of its slope, -3, which is .
To test whether this is correct, we can take first slope, , and multiply it with the negative reciprocal slope
:
Therefore, we came up with the correct slope for the other line, which is .
Finally, the y-intercept is given by (0, 5). Therefore, the equation of the line that is perpendicular to 3x + y = 3 is:
For 45, 45, 90 angled triangles, the two legs are equal to 'x', and the hypotenuse is equal to 
. Since we know the length of the hypotenuse, we can set this equal to it:
Divide the square root of 2 to both sides:
So the length of both AC and BC is approximately 5.657.
Divide the square root of 2 to both sides:
So the length of both AC and BC is approximately 5.657.