Consider the graph of each quadratic function.(a) Give the domain...

Question

Consider the graph of each quadratic function.(a) Give the domain and range.

Accepted Answer

Hello, everyone. We are asked to find the domain and range for the graph of the given quadratic function. The function we are given is F of X equals negative seven, multiplied by the parentheses X plus five squared plus seven. The graph is a P inverse of a parabola. And it's in quadrants two and three, recall the domain talks about all of the X values covered by the graph. So looking at our graph here, we're thinking about the domain. So does it ever stop going left or right? Does it ever stop expanding along the X axis? Well, we have nothing indicating that it ever does, which means that the domain would be all real numbers also written as negative infinity to positive infinity. The range is all of the Y values covered by the graph. So how far does it go up or down? And does it continue going down forever or up forever? Well, looking at our graph, we can see that it peaks, it has a maximum at the point negative 57. So this means that the graph never goes above the Y value of seven. So our range has to be all the values less than or equal to seven. So in interval notation, that would be a parentheses, negative infinity seven and then a square bracket. So now knowing our domain and range, we can look at our answer choices again, our domain was all real numbers. So went from negative infinity to positive infinity. So that means it's either answer choice B or C and then our range went from negative infinity to seven including seven. So we have a square bracket on seven. So this means this must be answer choice C where the domain is from negative infinity to positive infinity. And the range goes from negative infinity to seven including seven. Have a nice day.

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Consider the graph of each quadratic function.(a) Give the domain and range.