What's the relationship between (x)^1/2 and (x)^2? Based on their properties and graphs

If the point (-1/2, 1) is on the graph of f(x)=a(x-3)^2+50, what is the value of a?

write a formula for a function h(x), whose graph is identical to the graph of y=x^3 except that the graph of h has a hole at (2, 2^3). express the formula as a ratio of two polynomials

Explain what happens to the base function that went from  a(x)=x2 to f(x)=(x+3)^2

Given the function f(x)=(2)^x find the following functions of  -g(x) that shifts f(x) down 3 and to the left 6 -h(x) that reflects f(x) across the x-axis. please show solving steps for this problem.

Give a thorough analysis of the function f(x) = x^3 / (1+x)^2 , and sketch an accurate graph of the function.

x) = (1/3)x - 6

I need help with the rules for finding the difference quotient. for example. f(x)= 1/x^2

let f(g(x)) = 8(9 + 3/x^4+2)^7. Find the following functions.  if f(x) = 8x^7 then what is g(x)?  if g(x) = x^4 + 2 then what is f(x)?

When the function f(x) = 3(5)^x is changed to f(x) = 3(5)^x + 22, what is the effect? A.). There will be no change to the graph because the exponential portion of the function remains the same. B.) The y intercept is 22 spaces higher. C.) The x intercept is 22 spaces higher. D.) All the input values are moved 22 spaces to the right