Question

The graph of a quadratic function is shown. y equals to 4 if x is less than -4. y equals to 1 if -4 less than or equal to x less than -2. y equals to -2 if -2 less than or equal to x less than 0. y equals to -5 if 0 less than or equal to x less than 2. y equals to -1 if 2 less than or equal to x less than 4. y equals to 3 if x greater than or equal to 4. What is the minimum value of the function? A 4 B −2 C −8 D −9

Answer 1

The minimum value of the given piecewise-defined function is -5, occurring when x is between 0 and 2. Therefore correct option is E

Step-by-step explanation:

The question asks for the minimum value of a piecewise-defined quadratic function based on the given ranges of x and their corresponding y values. To find the minimum value, we look at the y values provided for each interval of x:

• y = 4 for x < -4
• y = 1 for -4 ≤ x < -2
• y = -2 for -2 ≤ x < 0
• y = -5 for 0 ≤ x < 2
• y = -1 for 2 ≤ x < 4
• y = 3 for x ≥ 4

The minimum value out of these is -5, which occurs when x is between 0 and 2. Therefore, the minimum value of the function is -5.

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The graph of a quadratic function is shown. y equals to 4 if x is less than -4. y equals to 1 if -4 less than or equal to x less than -2. y equals to -2 if -2 less than or equal to x less than 0. y equals to -5 if 0 less than or equal to x less than 2. y equals to -1 if 2 less than or equal to x less than 4. y equals to 3 if x greater than or equal to 4. What is the minimum value of the function?

A) 4 B)−2 C) −8 D) −9 E) -5