Problem 1
Show each of the following intervals on the real line. (a) \([-1,1]\) (b) \((-4,1]\) (c) \((-4,1)\) (d) \([1,4]\) (e) \([-1, \infty)\) (f) \((-\infty, 0]\)
Problem 1
In Problems 1-6, sketch a graph of the given exponential function. $$ f(x)=3^{x} $$
Problem 1
, plot the graph of each equation. Begin by checking for symmetries and be sure to find all \(x\) - and \(y\) -intercepts.. $$ y=-x^{2}+1 $$
Problem 1
For \(f(x)=x+3\) and \(g(x)=x^{2}\), find each value. (a) \((f+g)(2)\) (b) \((f \cdot g)(0)\) (c) \((g / f)(3)\) (d) \((f \circ g)(1)\) (e) \((g \circ f)(1)\) (f) \((g \circ f)(-8)\)
Problem 1
In Problems 1-16, simplify as much as possible. Be sure to remove all parentheses and reduce all fractions. $$ 4-2(8-11)+6 $$
Problem 1
In Problems \(1-4\), plot the given points in the coordinate plane and then find the distance between them. $$ (3,1),(1,1) $$
Problem 1
Convert the following degree measures to radians (leave \(\pi\) in your answer). (a) \(30^{\circ}\) (b) \(45^{\circ}\) (c) \(-60^{\circ}\) (d) \(240^{\circ}\) (e) \(-370^{\circ}\) (f) \(10^{\circ}\)
Problem 1
For \(f(x)=1-x^{2}\), find each value. (a) \(f(1)\) (b) \(f(-2)\) (c) \(f(0)\) (d) \(f(k)\) (e) \(f(-5)\) (f) \(f\left(\frac{1}{4}\right)\) (g) \(f(1+h)\) (h) \(f(1+h)-f(1)\) (i) \(f(2+h)-f(2)\)
Problem 1
find the exact value without using a calculator. $$ \arccos \left(\frac{\sqrt{2}}{2}\right) $$
Problem 2
For \(F(x)=x^{3}+3 x\), find each value. (a) \(F(1)\) (b) \(F(\sqrt{2})\) (c) \(F\left(\frac{1}{4}\right)\) (d) \(F(1+h)\) (e) \(F(1+h)-F(1)\) (f) \(F(2+h)-F(2)\)
