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Magazine Problem 123
For the following exercises, determine why the function \(f\) is discontinuous at a given point \(a\) on the graph. State which condition fails. $$ f(x)=\left\\{\begin{array}{ll}{3+x,} & {x<1} \\ {x,} & {x=1 \quad a=1} \\\ {x^{2},} & {x>1}\end{array}\right. $$
Problem 124
For the following exercises, determine why the function \(f\) is discontinuous at a given point \(a\) on the graph. State which condition fails. $$ f(x)=\left\\{\begin{array}{ll}{3-x,} & {x<1} \\ {x,} & {x=1 \quad a=1} \\ {2 x^{2},} & {x>1}\end{array}\right. $$
Problem 125
For the following exercises, determine why the function \(f\) is discontinuous at a given point \(a\) on the graph. State which condition fails. $$ f(x)=\left\\{\begin{array}{ll}{3+2 x,} & {x<1} \\ {x,} & {x=1 \quad a=1} \\\ {-x^{2},} & {x>1}\end{array}\right. $$
Problem 126
For the following exercises, determine why the function \(f\) is discontinuous at a given point \(a\) on the graph. State which condition fails. $$ f(x)=\left\\{\begin{array}{ll}{x^{2},} & {x<-2} \\ {2 x+1,} & {x=-2 \quad a=-2} \\ {x^{3},} & {x>-2}\end{array}\right. $$
Problem 127
For the following exercises, determine why the function \(f\) is discontinuous at a given point \(a\) on the graph. State which condition fails. $$ f(x)=\left\\{\begin{array}{ll}{\frac{x^{2}-9}{x+3},} & {x<-3} \\ {x-9,} & {x=-3 \quad a=-3} \\ {\frac{1}{x},} & {x>-3}\end{array}\right. $$
Problem 128
For the following exercises, determine why the function \(f\) is discontinuous at a given point \(a\) on the graph. State which condition fails. $$ f(x)=\left\\{\begin{array}{ll}{\frac{x^{2}-9}{x+3},} & {x<-3} \\ {x-9,} & {x=-3} \\ {-6,} & {x>-3}\end{array}\right. $$
Problem 129
For the following exercises, determine why the function \(f\) is discontinuous at a given point \(a\) on the graph. State which condition fails. $$ f(x)=\frac{x^{2}-4}{x-2}, \quad a=2 $$
Problem 130
For the following exercises, determine why the function \(f\) is discontinuous at a given point \(a\) on the graph. State which condition fails. $$ f(x)=\frac{25-x^{2}}{x^{2}-10 x+25}, \quad a=5 $$
Problem 131
For the following exercises, determine why the function \(f\) is discontinuous at a given point \(a\) on the graph. State which condition fails. $$ f(x)=\frac{x^{3}-9 x}{x^{2}+11 x+24}, \quad a=-3 $$
Problem 132
For the following exercises, determine why the function \(f\) is discontinuous at a given point \(a\) on the graph. State which condition fails. $$ f(x)=\frac{x^{3}-27}{x^{2}-3 x}, \quad a=3 $$
