Question

Caleb transformed the parent function f(x) = x^2 to create g(x) shown below. Which could be used to represent g(x)?

a. g(x) = f(x - 8.5)
b. g(x) = -8.5f(x)
c. g(x) = f(x + 8.5)
d. g(x) = f(x) - 8.5

Answer 1

Caleb transformed the parent function f(x) = x^2 to create g(x). Options a and c represent horizontal shifts to the right and left by 8.5 units, respectively, whereas option d represents a downward shift by 8.5 units. Option b represents scaling the function, which is not a horizontal shift.

Step-by-step explanation:

Caleb transformed the parent function f(x) = x^2 to create g(x). To determine which function represents g(x), we must understand how transformations affect the parent function. When a function is written as f(x - d), it translates the graph to the right by d units. When a function is f(x + d), the graph is translated to the left by d units. A function written as f(x) - k translates the graph down by k units.

If Caleb's function g(x) is a horizontal shift of the parent function, we might see an expression with f(x - d) or f(x + d). Option a, g(x) = f(x - 8.5), describes a shift of the parent function 8.5 units to the right. Option b, g(x) = -8.5f(x), represents scaling the function by -8.5, which is not a horizontal shift. Option c, g(x) = f(x + 8.5), describes a shift of the parent function 8.5 units to the left. Lastly, option d, g(x) = f(x) - 8.5, describes a downward shift by 8.5 units.