Question

choose the correct function/equation for the following description.
\ta constant function

choose the correct answer below.

a. $f(x) = 5x$

b. $f(x) = 3x + 6$

c. $f(x) = -8$

d. $f(x) = x^2$

Explanation:

A constant function is a function whose output value is the same for every input value. In other words, it has the form \( f(x) = c \), where \( c \) is a constant (a fixed real number). Let's analyze each option:

• Option A: \( f(x) = 5x \) is a linear function with a slope of 5, not a constant function.
• Option B: \( f(x) = 3x + 6 \) is a linear function with a slope of 3 and a y - intercept of 6, not a constant function.
• Option C: \( f(x)=- 8 \) is in the form \( f(x)=c \) (where \( c = - 8\)), so it is a constant function.
• Option D: \( f(x)=x^{2}\) is a quadratic function, not a constant function.

Answer:

C. \( f(x) = -8 \)