Find the domain and range of the function defined below: f(x) = \begin{cases} x+2 & \text{ for } x 4, \\ \frac{3}{4} x + 4 & \text{ for } x \geq 4. \end{cases} Find the domain and range of the function y = f(...
Find the domain algebraically without a graph of f(x) = \sqrt{4 - x^2}. We consider the function f(x, y) = \sqrt{3 - x^2 + y^2}. Find the domain of f. Consider the function f(x, y) = \sqrt{2 - x^2 + y^2}. Find the domain of f. ...
and can be represented as a list of ordered pairs, in words, algebraically, or graphically. When given the graph of a relation, we find the domain and range of the relation by first identifying the ordered pairs included in the graph of the relation. After doing this, we use the fol...
What will this look like when I try to find the inverse algebraically? The Vertical Line Test says that I can't have two y's that share an x-value. That is, each x has to have a UNIQUE corresponding y value. But look at what happens when I try to solve for "x=": My original...
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Algebraically, this can be represented by saying a function has a period p iff f(x)=f(x+p) for all x values in its domain. If a periodic function is continuous, then it must have a maximum and minimum value. The amplitude of a periodic function is half of the difference between its...
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A blouse that that is size x in the United States is size t(x) in Australia, where t(x) = 3x + 5. Find a function that will convert blouse sizes in Japan to blouse sizes in Australia. 3. For each of the following equations, ...
How do I find the line of symmetry?You can find the line of symmetry graphically or algebraically. To find the line of symmetry graphically, find the vertex, or the farthest point where two lines connect, and write either x = or y = and then insert the x- or y-coordinate.Which ...
The argument is basically this: As is well-known, the chain rule for first derivatives seems to follow algebraically if you use Leibniz notation for the derivatives: However, there’s a […] November 9, 2019 Hoping for Lane Closures Two lanes of a four lane highway are closed and you...