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Magazine Problem 5
Graph the given relation. $$ \left\\{\left(n, 4-n^{2}\right) \mid n=0,\pm 1,\pm 2\right\\} $$
Problem 5
Suppose (2,-3) is on the graph of \(y=f(x) .\) In Exercises \(1-18,\) use Theorem 1.7 to find a point on the graph of the given transformed function. $$ y=3 f(x) $$
Problem 5
Find an expression for \(f(x)\) and state its domain. \(f\) is a function that takes a real number \(x\) and performs the following three steps in the order given: (1) add \(3 ;\) (2) multiply by \(2 ;\) (3) take the square root.
Problem 5
Find the indicated intersection or union and simplify if possible. Express your answers in interval notation. $$ (-\infty, 0) \cap[1,5] $$
Problem 6
Graph the given relation. $$ \\{(\sqrt{j}, j) \mid j=0,1,4,9\\} $$
Problem 6
In Exercises \(1-12\), sketch the graph of the given function. State the domain of the function, identify any intercepts and test for symmetry. $$ f(x)=x^{3} $$
Problem 6
Find an expression for \(f(x)\) and state its domain. \(f\) is a function that takes a real number \(x\) and performs the following three steps in the order given: (1) add \(3 ;(2)\) take the square root; (3) multiply by 2 .
Problem 6
Use the pair of functions \(f\) and \(g\) to find the following values if they exist. \- \((f+g)(2)\) \- \((f g)\left(\frac{1}{2}\right)\) -\((f-g)(-1)\) -\(\left(\frac{f}{g}\right)(0)\) -\((g-f)(1)\) -\(\left(\frac{g}{f}\right)(-2)\) $$f(x)=\sqrt{4-x} \text { and } g(x)=\sqrt{x+2}$$
Problem 6
Suppose (2,-3) is on the graph of \(y=f(x) .\) In Exercises \(1-18,\) use Theorem 1.7 to find a point on the graph of the given transformed function. $$ y=f(3 x) $$
Problem 6
Determine whether or not the relation represents \(y\) as a function of \(x .\) Find the domain and range of those relations which are functions. $$ \\{(x, 1) \mid x \text { is an irrational number }\\} $$
