Question

Which graph represents the following piecewise defined function?

a) Q(x) = -2x for x < -25%, x^4 - 2 for -25% ≤ x < 1, x for x ≥ 1
b) Q(x) = -2x for x < 1, x^4 - 2 for -25% ≤ x < 1, x for x ≥ 1
c) Q(x) = -2x for -25% ≤ x < 1, x^4 - 2 for x ≥ 1
d) Q(x) = -2x for x < -25%, x^4 - 2 for x ≥ 1

Answer 1

The graph that correctly represents the given piecewise defined function (Q(x) = -2x for x < -25%, Q(x) = x^4 - 2 for -25% ≤ x < 1, Q(x) = x for x ≥ 1) is option b, which illustrates each segment according to its respective rule.

Step-by-step explanation:

When analyzing piecewise defined functions, each segment of the function is defined by a specific rule depending on the range of the input variable x. A correct graph for a piecewise defined function will show different behaviors, such as linear, polynomial, or constant functions, for different intervals of x. In this specific case, we have to find the graph that correctly represents the given piecewise function:

• Q(x) = -2x for x < -25%
• Q(x) = x^4 - 2 for -25% ≤ x < 1
• Q(x) = x for x ≥ 1

To find the correct answer, we need to look at the definitions of Q(x) and identify which graph shows:

1. A line with a negative slope for x < -25%
2. A quartic function (x raised to the fourth power) subtracted by 2 between x = -25% and x < 1
3. A linear function with a slope of 1 for x ≥ 1

The answer that matches these criteria is

option b

.