Answer:
There's no image.................
Answer:
A
Step-by-step explanation:
because A is a Equivalent when you times it by 4
Answer:
(-3,4)
Step-by-step explanation:
That means to reflect the point across the y-axis... If you draw (3,4) on the coordinate plane you should see (-3,4) is the reflection across the y-axis from that point.
Answer:
the answer is 8, the distance between -11 and -3 is 8
Step-by-step explanation:
if you count the between the numbers it's a total of 8
Answer:
![k=1/9](https://tex.z-dn.net/?f=k%3D1%2F9)
Step-by-step explanation:
A function is continuous at a point if and only if:
![\lim_{x \to n} f(x)=f(n)](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20n%7D%20f%28x%29%3Df%28n%29)
So, we have the piecewise function:
![f(x) = \left\{ \begin{array}{lI} \frac{\sqrt{x} -3}{-9} & \quad0< x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cleft%5C%7B%20%20%20%20%20%20%20%20%5Cbegin%7Barray%7D%7BlI%7D%20%20%20%20%20%20%20%20%20%20%20%20%5Cfrac%7B%5Csqrt%7Bx%7D%20-3%7D%7B-9%7D%20%26%20%5Cquad0%3C%20x%20%3C9%20%5C%5C%20%20%20%20%20%20%20%20%20%20%20%201-kx%20%26%20%5Cquad%20x%5Cgeq%209%20%20%20%20%20%20%20%20%5Cend%7Barray%7D%20%20%20%20%5Cright.%24%24)
And we want to find the value of k such that the function is continuous.
First, find the left hand limit of f(x):
![\lim_{x\to9^-} f(x)](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto9%5E-%7D%20f%28x%29)
Since we're coming from the left, we'll use the first equation. Thus:
![=\lim_{x\to9^-} \frac{\sqrt{x}-3}{-9}](https://tex.z-dn.net/?f=%3D%5Clim_%7Bx%5Cto9%5E-%7D%20%5Cfrac%7B%5Csqrt%7Bx%7D-3%7D%7B-9%7D)
Direct substitution:
![=\frac{\sqrt{9}-3}{-9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Csqrt%7B9%7D-3%7D%7B-9%7D)
Simplify:
![=\frac{3-3}{-9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3-3%7D%7B-9%7D)
Subtract and divide:
![=\frac{0}{-9}=0](https://tex.z-dn.net/?f=%3D%5Cfrac%7B0%7D%7B-9%7D%3D0)
So, what this tells us is that for the function to be continuous, the right hand limit as f(x) approaches 9 from the right <em>must</em> also be equal to 0.
Therefore:
![\lim_{n \to 9^+} 1-kx=0](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%209%5E%2B%7D%201-kx%3D0)
Direct substitution:
![1-9k=0](https://tex.z-dn.net/?f=1-9k%3D0)
Subtract 1 from both sides:
![-9k=-1](https://tex.z-dn.net/?f=-9k%3D-1)
Divide both sides by -9:
![k=1/9](https://tex.z-dn.net/?f=k%3D1%2F9)
Therefore, the value of k is 1/9.
So, our equation in the end is:
![f(x) = \left\{ \begin{array}{lI} \frac{\sqrt{x} -3}{-9} & \quad0< x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cleft%5C%7B%20%20%20%20%20%20%20%20%5Cbegin%7Barray%7D%7BlI%7D%20%20%20%20%20%20%20%20%20%20%20%20%5Cfrac%7B%5Csqrt%7Bx%7D%20-3%7D%7B-9%7D%20%26%20%5Cquad0%3C%20x%20%3C9%20%5C%5C%20%20%20%20%20%20%20%20%20%20%20%201-%5Cfrac%7B1%7D%7B9%7Dx%20%26%20%5Cquad%20x%5Cgeq%209%20%20%20%20%20%20%20%20%5Cend%7Barray%7D%20%20%20%20%5Cright.%24%24)