Chapter 8

If \(P(x)=x^{2}+x+1\) and \(Q(x)=5 x^{2}-1,\) find each function value. $$ P(7) $$

Sketch the graph of each function. $$ f(x)=|x|+3 $$

Find the domain and the range of each relation. Also determine whether the relation is a function. $$ \\{(-1,7),(0,6),(-2,2),(5,6)\\} $$

Write an equation of each line with the given slope and containing the given point. Write the equation in the slope-intercept form \(y=m x+b .\) See Example \(1 .\) Slope \(3 ;\) through (1,2)

Graph the solution set of each inequality on a number line and then write it in interval notation. $$ \\{x \mid x<-3\\} $$

If \(P(x)=x^{2}+x+1\) and \(Q(x)=5 x^{2}-1,\) find each function value. $$ Q(4) $$

Sketch the graph of each function. $$ f(x)=|x|-2 $$

Find the domain and the range of each relation. Also determine whether the relation is a function. $$ \\{(4,9),(-4,9),(2,3),(10,-5)\\} $$

Write an equation of each line with the given slope and containing the given point. Write the equation in the slope-intercept form \(y=m x+b .\) See Example \(1 .\) Slope 4 ; through (5,1)

Graph the solution set of each inequality on a number line and then write it in interval notation. $$ \\{x \mid x>5\\} $$

If \(P(x)=x^{2}+x+1\) and \(Q(x)=5 x^{2}-1,\) find each function value. $$ Q(-10) $$

Sketch the graph of each function. $$ f(x)=\sqrt{x}-2 $$

Find the domain and the range of each relation. Also determine whether the relation is a function. $$ \\{(-2,4),(6,4),(-2,-3),(-7,-8)\\} $$

Write an equation of each line with the given slope and containing the given point. Write the equation in the slope-intercept form \(y=m x+b .\) See Example \(1 .\) Slope \(-2 ;\) through (1,-3)

Graph the solution set of each inequality on a number line and then write it in interval notation. $$ \\{x \mid x \geq 0.3\\} $$

If \(P(x)=x^{2}+x+1\) and \(Q(x)=5 x^{2}-1,\) find each function value. $$ P(-4) $$

Sketch the graph of each function. $$ f(x)=\sqrt{x}+3 $$

Find the domain and the range of each relation. Also determine whether the relation is a function. $$ \\{(6,6),(5,6),(5,-2),(7,6)\\} $$

Write an equation of each line with the given slope and containing the given point. Write the equation in the slope-intercept form \(y=m x+b .\) See Example \(1 .\) Slope \(-4 ;\) through (2,-4)

Graph the solution set of each inequality on a number line and then write it in interval notation. $$ \\{x \mid x<-0.2\\} $$

If \(P(x)=x^{2}+x+1\) and \(Q(x)=5 x^{2}-1,\) find each function value. $$ P(0) $$

Sketch the graph of each function. $$ f(x)=|x-4| $$

Find the domain and the range of each relation. Also determine whether the relation is a function. $$ \\{(1,1),(1,2),(1,3),(1,4)\\} $$

Write an equation of each line with the given slope and containing the given point. Write the equation in the slope-intercept form \(y=m x+b .\) See Example \(1 .\) Slope \(\frac{1}{2} ;\) through (-6,2)

Graph the solution set of each inequality on a number line and then write it in interval notation. $$ \\{x \mid-7 \leq x\\} $$

If \(P(x)=x^{2}+x+1\) and \(Q(x)=5 x^{2}-1,\) find each function value. $$ Q(0) $$

Sketch the graph of each function. $$ f(x)=|x+3| $$

Find the domain and the range of each relation. Also determine whether the relation is a function. $$ \\{(1,1),(2,1),(3,1),(4,1)\\} $$

Write an equation of each line with the given slope and containing the given point. Write the equation in the slope-intercept form \(y=m x+b .\) See Example \(1 .\) Slope \(\frac{2}{3} ;\) through (-9,4)

Graph the solution set of each inequality on a number line and then write it in interval notation. $$ \\{x \mid-7 \geq x\\} $$

If \(P(x)=x^{3}+2 x-3\) and \(Q(x)=7 x+5,\) find each function value. $$ P(2) $$

Sketch the graph of each function. $$ f(x)=\sqrt{x+2} $$

Find the domain and the range of each relation. Also determine whether the relation is a function. $$ \left\\{\left(\frac{3}{2}, \frac{1}{2}\right),\left(1 \frac{1}{2},-7\right),\left(0, \frac{4}{5}\right)\right\\} $$

Write an equation of each line with the given slope and containing the given point. Write the equation in the slope-intercept form \(y=m x+b .\) See Example \(1 .\) Slope \(-\frac{9}{10} ;\) through (-3,0)

Graph the solution set of each inequality on a number line and then write it in interval notation. $$ \\{x \mid-2

If \(P(x)=x^{3}+2 x-3\) and \(Q(x)=7 x+5,\) find each function value. $$ Q(6) $$

Sketch the graph of each function. $$ f(x)=\sqrt{x-2} $$

Find the domain and the range of each relation. Also determine whether the relation is a function. $$ \left\\{\left(\frac{1}{2}, \frac{1}{4}\right),\left(0, \frac{7}{8}\right),(0.5, \pi)\right\\} $$

Write an equation of each line with the given slope and containing the given point. Write the equation in the slope-intercept form \(y=m x+b .\) See Example \(1 .\) Slope \(-\frac{1}{5} ;\) through (4,-6)

Graph the solution set of each inequality on a number line and then write it in interval notation. $$ \\{x \mid-5 \leq x \leq-1\\} $$

If \(P(x)=x^{3}+2 x-3\) and \(Q(x)=7 x+5,\) find each function value. $$ Q(-3) $$

Sketch the graph of each function. $$ y=(x-4)^{2} $$

Find the domain and the range of each relation. Also determine whether the relation is a function. $$ \\{(-3,-3),(0,0),(3,3)\\} $$

Write an equation of the line passing through the given points. Write the equation in standard form \(A x+B y=C\). See Example 2 . (2,0) and (4,6)

Graph the solution set of each inequality on a number line and then write it in interval notation. $$ \\{x \mid 5 \geq x>-1\\} $$

If \(P(x)=x^{3}+2 x-3\) and \(Q(x)=7 x+5,\) find each function value. $$ P(-1) $$

Sketch the graph of each function. $$ y=(x+4)^{2} $$

Find the domain and the range of each relation. Also determine whether the relation is a function. $$ \\{(\pi, 0),(0, \pi),(-2,4),(4,-2)\\} $$

Write an equation of the line passing through the given points. Write the equation in standard form \(A x+B y=C\). See Example 2 . (3,0) and (7,8)

Graph the solution set of each inequality on a number line and then write it in interval notation. $$ \\{x \mid-3>x \geq-7\\} $$