For the given expressions we will have:
y = exp(x - 4) →we have a shift of 4 units to the right.
y = exp (x +9) → we have a shift of 9 units to the left.
y = exp(x) + 7 → we have a shift of 7 units up.
y = exp(x) - 6 → we have a shift of 6 units down.
<h3>
How to work with vertical and horizontal shifts?</h3>
Remember that the shifts work as follows.
For a function f(x), we define a vertical shift of N units as:
g(x) = f(x) + N
- If N > 0, the shift is upwards.
- If N < 0, the shift is downwards.
For a function f(x), we define a horizontal shift of N units as:
g(x) = f(x + N)
- If N > 0, the shift is to the left.
- If N < 0, the shift is to the right.
Then, if we have:
exp(x - 4) we have a shift of 4 units to the right.
exp (x +9) we have a shift of 9 units to the left.
exp(x) + 7 we have a shift of 7 units up.
exp(x) - 6 we have a shift of 6 units down.
Learn more about translations
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Answer:
Y=√2
Step-by-step explanation:
We can use the pathagorian theorum: A²+B²=C² now in this case it would be X²+Y²=2² we also know that X and Y are the same number in this problem because they have the same corresponding angle (triangle angles always add to 180 and since we know 2 of the angles are 45 and 90 the remaining angle will also be 45) Because of this we can change our equation to Z²+Z²=2² (I'm using Z so that we do not confuse it with another letter we've already used) from there we can go to Z∧4=2² and then we will solve the equation. Z=√2 Z also equals X and Y therefore Y=√2
I hope this helps and please let me know if there is anything you don't understand I would be happy to clarify!
Answer:
Step-by-step explanation:
Equation
3x + 9 + 2x = x - 2x - 3
Solution
Combine all the like terms.
3x+2x+9 = x - 2x - 3
5x + 9 = -x - 3 Add x to both sides of the equation
5x+x +9 = -x+x -3 Combine
6x + 9 = - 3 Subtract 9 from both sides of the equation
6x+9-9 = - 3-9 Combine
6x = -12 Divide both sides by 6
6x/6 = -12/6
x = - 2
Answer x = - 2
<span>So, the volume of a container can also be thought of as the amount of liquid that the container is capable of holding. It follows that 450=(length)(width)(height). The constraints of the problem say that the length of the box must be twice as large as the width, so it follows that j(height)=(2w)(w)(height)-450. This then implies that j(height)=(2w^2)(height)-450. In simpler terms, the height is defined as 450/(2w^2), or j(w)=450/(2w^2).</span>
