Use the information provided to answer Part A and Part B.
The function f(x) = 4x - x² is graphed in the x-y coordinate plane as shown.
The function f(x) = 4x - x² is graphed in the x-y coordinate plane as shown.
Part A
Based on the graph of the function, which statements are true? Select all that apply. A.) f is increasing on the interval x < 0 B.) f is decreasing on the interval x < 0 C.) f is increasing on the interval 0 < x < 2 D.) f is decreasing on the interval 0 < x < 2 E.) f is increasing on the interval 2 < x < 4 F.) f is decreasing on the interval 2 < x < 4 G.) f is increasing on the interval x > 4 H.) f is decreasing on the interval x > 4 |
Part B
Based on the graph of the function, which statements are true? Select all that apply. A.) f(x) < 0 on the interval x < 0 B.) f(x) > 0 on the interval x < 0 C.) f(x) < 0 on the interval 0 < x < 2 D.) f(x) > 0 on the interval 0 < x < 2 E.) f(x) < 0 on the interval 2 < x < 4 F.) f(x) > 0 on the interval 2 < x < 4 G.) f(x) < 0 on the interval x > 4 H.) f(x ) > 0 on the interval x > 4 |
Part A.
Looking at the graph, you can see the function is increasing (rising) as x moves from - ∞ to 2. Also, the function is decreasing (falling) as x moves from 2 to + ∞. Therefore, true statements include: A.) f is increasing on the interval x < 0 C.) f is increasing on the interval 0 < x < 2 F.) f is decreasing on the interval 2 < x < 4 H.) f is decreasing on the interval x > 4 Ask Algebra House |
Part B.
Looking at the graph, you can see f(x) (the y-value) is greater than zero for x-values between 0 and 4. Also, f(x) is less than zero when x < 0 and when x > 4. Therefore, true statements include: A.) f(x) < 0 on the interval x < 0 D.) f(x) > 0 on the interval 0 < x < 2 F.) f(x) > 0 on the interval 2 < x < 4 G.) f(x) < 0 on the interval x > 4 |