Q&A for How to Find the Range of a Function

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What is range on a graph?

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Expert Answer

The range is all of the possible y values that can exist on a graph. What are all of the numbers that could successfully be plugged in as y coordinates? What are all of the places that the graph vertically touches? Answering these questions helps you find the range of a graph.

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How can I find range of a function using limits?

Community Answer

If a function doesn't have a maximum (or a minimum), then you might have to evaluate a limit to find its range. For example, f(x) = 2^x doesn't have a minimum but the limit as x approaches negative infinity is 0, and the limit as x approaches positive infinity is infinity. So the range is (0,infinity) using open intervals because neither limit is ever reached, only approached.

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What is AM = GM concept for finding range?

Community Answer

This refers to the Arithmetic Mean (AM) - Geometric Mean (GM) inequality, which states that for positive numbers, the AM is always at least as large as the GM. In some cases, this can be used to find upper or lower bounds for the range of a function. For example, find the range of f(x) = x^2 + 1/x^2. It obviously has a minimum, but where? Many calculus students will immediately take a derivative. This works fine, but if you know the AM-GM inequality, there is no need for the heavy artillery of calculus. f(x) = 2 * AM(x^2, 1/x^2). The GM of (x^2, 1/x^2) is 1, and the since the AM is more than that, f(x) is always at least 2, and the range of f is [2, infinity).

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The function is given that g(x)=x2-5x+9. How do I find the values of x, which have an image of 15?

Community Answer

Simply put g(x) = 15, you will get 2 values of 'x' which satisfy the given quadratic equation. Those values are your answer.

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How do I find the range of a parabola when it is off of the x or y axis (for instance x=3)?

Community Answer

Start by finding the vertex. If the parabola is the form a(x-h)^2+k, then (h,k) is the vertex. If it is not in that form but rather in ax^2+bx+c, then get it in the standard form or graph it. From the vertex, if the parabola opens up, then the range will be (k, infinity) and if it opens down the range will be (-infinity, k).

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What is the range of y=-4*-3 when the domain is (-1,0,2)?

Community Answer

Substitute the elements in the domain to x. The values of y you are getting are the elements of the range.

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Question

How do I find the range of an equation?

Donagan

Top Answerer

It's the same as finding the range of a function, as shown above. (This article refers to equations as "functions.")

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If f(x) = 2x + 4, how can I find the range?

Surekha Pallemmedi

Community Answer

If x =1 then f(x) is =6.if x= 2 then f(x) =8 here range is 6,8.

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