SOLUTION: Consider the function g(x) = -2(2) ^ ½(x+2) + 3. What is the base (parent) function? Write the mapping rule that transforms the base function to g(x) Complete a table of value

Algebra ->  Graphs -> SOLUTION: Consider the function g(x) = -2(2) ^ ½(x+2) + 3. What is the base (parent) function? Write the mapping rule that transforms the base function to g(x) Complete a table of value      Log On


   

Question 1203062: Consider the function g(x) = -2(2) ^ ½(x+2) + 3.
What is the base (parent) function?
Write the mapping rule that transforms the base function to g(x)
Complete a table of values for 5 points on your base function and
transformed function
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the function g(x) = -2(2) ^ ½(x+2) + 3.
What is the base (parent) function? 
p%28x%29=2%5Ex <--base (parent) function
graph%28400%2C400%2C-5%2C5%2C-2%2C8%2C2%5Ex%29matrix%286%2C2%2Cx%2Cy%2C-2%2C0.25%2C-1%2C0.5%2C0%2C1%2C1%2C2%2C2%2C4%29
matrix%282%2C1%2C%22%22%2Cy=p%28expr%281%2F2%29x%29=2%5E%28expr%281%2F2%29x%29%29 <-- multiplying x by 1%2F2 stretches graph horizontally by a factor of 1%5E%22%22%2F%281%2F2%29=2
graph%28400%2C400%2C-5%2C5%2C-2%2C8%2C2%5E%280.5x%29%29matrix%286%2C2%2Cx%2Cy%2C-2%2C0.5%2C-1%2C0.707%2C0%2C1%2C1%2C1.414%2C2%2C2%29
 <-- adding 2 to x shifts graph left 2 units.
graph%28400%2C400%2C-5%2C5%2C-2%2C8%2C2%5E%280.5%28x%2B2%29%29%29matrix%286%2C2%2Cx%2Cy%2C-2%2C1%2C-1%2C1.414%2C0%2C2%2C1%2C2.83%2C2%2C4%29
 <-- multiplying entire right side by 2 stretches graph vertically by a factor of 2.
graph%28400%2C400%2C-5%2C5%2C-2%2C8%2C2%2A2%5E%280.5%28x%2B2%29%29%29matrix%286%2C2%2Cx%2Cy%2C-2%2C2%2C-1%2C2.828%2C0%2C4%2C1%2C5.657%2C2%2C8%29
 <-- multiplying the entire right side by -1 reflects graph across the x-axis.
graph%28400%2C400%2C-5%2C5%2C-8%2C2%2C-2%2A2%5E%280.5%28x%2B2%29%29%29matrix%286%2C2%2Cx%2Cy%2C-2%2C-2%2C-1%2C-2.828%2C0%2C-4%2C1%2C-5.657%2C2%2C-8%29
 <-- adding 3 to the entire right side shifts  graph upward 3 units.
graph%28400%2C400%2C-5%2C5%2C-8%2C2%2C-2%2A2%5E%280.5%28x%2B2%29%29%2B3%29matrix%286%2C2%2Cx%2Cy%2C-2%2C1%2C-1%2C0.172%2C0%2C-1%2C1%2C-2.657%2C2%2C-5%29

The mapping rule from base (parent) function p(x) to g(x) is %22g%28x%29%22=-2p%28expr%281%2F2%29%28x-2%29%29%2B3

Edwin