91Ó°ÊÓ

An equation of the form \(|f(x)|=|g(x)|\) is given. (a) Solve the equation analytically and support the solution graphically. (b) Solve \(|f(x)|>|g(x)|\) (c) Solve \(|f(x)|<|g(x)|\) $$|4 x+1|=|4 x+6|$$

Let the domain of \(f(x)\) be \([-1,2]\) and the range be \([0,3] .\) Find the domain and range of the following. $$-2 f(-x)$$

An equation of the form \(|f(x)|=|g(x)|\) is given. (a) Solve the equation analytically and support the solution graphically. (b) Solve \(|f(x)|>|g(x)|\) (c) Solve \(|f(x)|<|g(x)|\) $$|6 x+9|=|6 x-3|$$

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the \(y\) -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion. $$f(x)=|-x|$$

Let the domain of \(f(x)\) be \([-1,2]\) and the range be \([0,3] .\) Find the domain and range of the following. $$f(-3 x)$$

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the \(y\) -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion. $$f(x)=\frac{1}{4 x^{3}}$$

An equation of the form \(|f(x)|=|g(x)|\) is given. (a) Solve the equation analytically and support the solution graphically. (b) Solve \(|f(x)|>|g(x)|\) (c) Solve \(|f(x)|<|g(x)|\) $$|0.25 x+1|=|0.75 x-3|$$

For each function find \(f(x+h)\) and \(f(x)+f(h)\). $$f(x)=x^{2}-4$$

Let the domain of \(f(x)\) be \([-1,2]\) and the range be \([0,3] .\) Find the domain and range of the following. $$\frac{1}{3} f(x-3)$$

For each function find \(f(x+h)\) and \(f(x)+f(h)\). $$f(x)=5 x^{2}+x$$