Use the graph to answer the question.
The figure shows the graph of the function y equals left-parenthesis x minus 1 right-parenthesis squared minus 4. Identify the x-values for which the function is increasing.
(1 point)
Responses
left-parenthesis x vertical line x greater than negative 4 right-parenthesis
Image with alt text: left-parenthesis x vertical line x greater than negative 4 right-parenthesis
left-parenthesis x vertical line x less than negative 1 or x greater than 3 right-parenthesis
Image with alt text: left-parenthesis x vertical line x less than negative 1 or x greater than 3 right-parenthesis
left-parenthesis x vertical line x greater than 1 right-parenthesis
Image with alt text: left-parenthesis x vertical line x greater than 1 right-parenthesis
left-parenthesis x vertical line x greater-than-or-equal to 0 right-parenthesis
The correct answer is:
left-parenthesis x vertical line x greater than 1 right-parenthesis.
To identify the x-values for which the function is increasing, we need to look for regions on the graph where the y-values are moving upward as we move from left to right. This corresponds to finding where the slope of the function is positive.
Looking at the graph of the function y = (x - 1)^2 - 4, we can observe that the graph opens upward, forming a U-shape.
In general, for a quadratic function in the form y = ax^2 + bx + c, if the coefficient "a" is positive, the graph will open upward, and if "a" is negative, the graph will open downward.
In our case, since the coefficient of x^2 is positive (a = 1), the graph opens upward.
Therefore, the function is increasing for x-values in the intervals where the graph is rising.
Looking at the graph, we can see that the graph rises to the left of x = 1 and also to the right of x = 1. So, the function is increasing for x > 1 and x < -1.
Therefore, the correct answer is: (x vertical line x greater than 1) or (x vertical line x less than -1).
To identify the x-values for which the function is increasing, we need to look for the parts of the graph where the function is sloping upwards.
By examining the graph, we can see that the function is increasing in two intervals:
1. From left-parenthesis x vertical line x greater than negative 4 right-parenthesis
2. From left-parenthesis x vertical line x greater than 1 right-parenthesis
Therefore, the correct answer is:
- left-parenthesis x vertical line x greater than negative 4 right-parenthesis
- left-parenthesis x vertical line x greater than 1 right-parenthesis