Question
A.) True or False: Linear functions are ALWAYS increasing or decreasing but never both.
B.) True or False: Quadratic functions will ALWAYS have one interval of increasing and one interval of decreasing.
C.) True or False: Exponential functions are always increasing.
B.) True or False: Quadratic functions will ALWAYS have one interval of increasing and one interval of decreasing.
C.) True or False: Exponential functions are always increasing.
Answers
GPT-4o mini
A.) True: Linear functions have a constant rate of change, which means they are either always increasing (positive slope) or always decreasing (negative slope), but never both.
B.) False: Quadratic functions can have one interval of increasing and one interval of decreasing, but they can also be constant at a vertex (in the case of a perfect square, where the vertex is the minimum or maximum point). Thus, there are cases where they do not have both intervals.
C.) True: Exponential functions of the form \( f(x) = a \cdot b^x \) (where \( a > 0 \) and \( b > 1 \)) are always increasing for positive bases. If the base is between 0 and 1, the function will always be decreasing. However, in a general sense (considering cases with bases greater than 1), they are typically described as always increasing.
B.) False: Quadratic functions can have one interval of increasing and one interval of decreasing, but they can also be constant at a vertex (in the case of a perfect square, where the vertex is the minimum or maximum point). Thus, there are cases where they do not have both intervals.
C.) True: Exponential functions of the form \( f(x) = a \cdot b^x \) (where \( a > 0 \) and \( b > 1 \)) are always increasing for positive bases. If the base is between 0 and 1, the function will always be decreasing. However, in a general sense (considering cases with bases greater than 1), they are typically described as always increasing.