The graph of f(x)-x^2 is horizontally stretched by a factor of 3, and then shifted shifted to the left 2 units and down 2 units. Which equation describes the function g that results?
-g(x) = (((x-2)/3) - 2)^2
-g(x) = (3(x-2)))^2 + 2
-g(x) = (3(x+2))^2 - 2
-g(x) = ((x+2)/3)^2 - 2
-g(x) = (((x-2)/3)^2 + 2
g(x) = (((x+2)/3)^2) - 2
Would be my answer. Am I wrong or right sir?
The correct equation that describes the function g is:
-g(x) = (((x-2)/3) - 2)^2
To horizontally stretch a function, you would divide the x-values by the scaling factor. In this case, the scaling factor is 3. So, to horizontally stretch the function f(x) by a factor of 3, you would use the equation f((x-2)/3).
To shift the function to the left, you would subtract the shift amount from the x-values. In this case, the function is shifted 2 units to the left. So, we need to subtract 2 from the expression (x-2)/3, resulting in (x-2-2)/3 = (x-4)/3.
To shift the function down, you would subtract the shift amount from the y-values. In this case, the function is shifted 2 units down. So, we need to subtract 2 from the expression (x-4)/3, resulting in ((x-4)/3) - 2.
Finally, to get the equation for the function g(x), we need to negate the entire expression since the question asks for -g(x). This gives us -(((x-4)/3) - 2).
Simplifying this equation further, we have:
-g(x) = -(((x-4)/3) - 2)
= -((x-4)/3) + 2
= -((x-4)/3) + 2(3/3)
= -((x-4)/3) + 6/3
= (-x + 4)/3 + 6/3
= (-x + 4 + 6)/3
= (-x + 10)/3
Therefore, the equation that describes the function g resulting from stretching f(x)-x^2 by a factor of 3, shifting 2 units to the left, and 2 units down is -g(x) = (-x + 10)/3.