Question

Which function represents a reflection of f(x)=5(0.8x+2) across the x-axis?

a) g(x)=5(0.87x)
b) g(x)=−5(0.87x)
c) g(x)=(0.88x)
d) g(x)=5(−0.89x)

Answer 1

The correct reflection of the function f(x) = 5(0.8x+2) across the x-axis would be g(x) = -5(0.8x+2). None of the options provided match this transformation, as reflections across the x-axis require negating the entire function.

Step-by-step explanation:

To find a function that is a reflection of another function across the x-axis, you must negate the y values of the function. The function f(x) = 5(0.8x+2) becomes g(x) = -5(0.8x+2) under reflection across the x-axis. None of the options provided in the question accurately reflects this transformation. The correct reflection would simply multiply the original function by -1.

Reflections can change the characteristics of a function, such as turning maximum points into minimum points on a graph and vice versa, but they preserve the shape of the original function's graph. If f(x) represents the original function, then a reflection across the x-axis is given by g(x) = -f(x).