Can I see the full problem from the worksheet?your work looks correct to me.
AP teachers for<span> course and exam preparation; permission </span>for<span> any other use ... 3. Question 2. Let f and g be the functions given by ( ). (. ) 2 1. </span>f x<span> x x. = − and. ( ) (. ) ..... </span>Let f be the function given by<span> ( ). ( ) </span>sin<span> 5. ,. </span>4<span>. </span>f x<span> x </span>π<span>. = + and let ( ). P x be the ...</span>
Answer:
1. The circumference of any circle equals two times its radius multiplied by pi (π, approximately 3.14). We can also say it equals pi times its diameter.
Thank you
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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