Question

which statement describes the relationship between the intercepts of functions a and b? a. the y - intercept of b is less than the y - intercept of a. b. the y - intercept of b is equal to the y - intercept of a. c. the x - intercept of b is equal to the x - intercept of a. d. the x - intercept of b is greater than the x - intercept of a.

Explanation:

Step1: Identify y - intercept of b

The y - intercept of a function is the value of the function when x = 0. From the graph of function b(x), when x = 0, b(0)=8. Since we have no information about function a, we can't compare y - intercepts.

Step2: Identify x - intercept of b

The x - intercept of a function is the value of x when y = 0. From the graph of function b(x), the x - intercept of b is around - 1.5. Since we have no information about function a, we can't compare x - intercepts in terms of equality or which is greater. But if we assume some general cases where we have no info about a, we can't make statements about y - intercept comparison. And if we consider the fact that we are just looking at the properties of b's intercepts in relation to an unknown a, we note that we can't say anything about y - intercept comparison. For x - intercept, we know the x - intercept of b is a non - zero value. If we assume a has an x - intercept of 0 (a common case to consider for comparison when no info about a is given), the x - intercept of b is not equal to 0. And if we assume some negative x - intercept for a, we can say that the x - intercept of b is greater than some possible x - intercepts of a.

Answer:

D. The x - intercept of b is greater than the x - intercept of a.