Chapter 2

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$f(x)=\left|\frac{x}{2}\right|$$

Factor to find the \(x\)-intercepts of the parabola described by the quadratic function. Also find the real zeros of the function. $$h(t)=-3 t^{2}+10 t-8$$

Solve the inequality by factoring. $$-x^{2}+2 x-1<0$$

Solve the rational equation. Check your solutions. $$\frac{3}{x+1}+\frac{2}{x-3}=4$$

Find the real and imaginary parts of the complex number. $$1+\sqrt{-5}$$

Use transformations to graph the quadratic function and find the vertex of the associated parabola. $$f(x)=(x+2)^{2}-1$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$(h-f)(-1)$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$f(x)=(2 x)^{2}$$

Find a possible expression for a quadratic function \(f(x)\) having the given zeros. There can be more than one correct answer. $$x=1 \text { and } x=-3$$

Solve the inequality by factoring. $$x^{2}+4 x+4>0$$

Solve the rational equation. Check your solutions. $$\frac{1}{2 x-3}-\frac{x}{x-1}=2$$

Find the real and imaginary parts of the complex number. $$\sqrt{-7}-1$$

Use transformations to graph the quadratic function and find the vertex of the associated parabola. $$h(x)=(x-3)^{2}+2$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$(h-f)(0)$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$f(x)=\left(\frac{1}{2} x\right)^{2}$$

Find a possible expression for a quadratic function \(f(x)\) having the given zeros. There can be more than one correct answer. $$x=-2 \text { and } x=4$$

Solve the inequality algebraically or graphically. $$2 x^{2}-3 x<1$$

Solve the rational equation. Check your solutions. $$\frac{1}{x^{2}-x-6}+\frac{3}{x+2}=\frac{-4}{x-3}$$

Find the complex conjugate of each number. $$-2$$

Use transformations to graph the quadratic function and find the vertex of the associated parabola. $$f(x)=-(x+1)^{2}-1$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$(f g)(3)$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$g(x)=\sqrt{3 x}$$

Find a possible expression for a quadratic function \(f(x)\) having the given zeros. There can be more than one correct answer. $$x=-3 \text { and } x=0$$

Solve the inequality algebraically or graphically. $$-x^{2}-3 x>-1$$

Solve the rational equation. Check your solutions. $$\frac{1}{x^{2}+4 x-5}+\frac{6}{x+5}=\frac{1}{x-1}$$

Find the complex conjugate of each number. $$-5$$

Use transformations to graph the quadratic function and find the vertex of the associated parabola. $$g(s)=-(s-2)^{2}+2$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$(f g)(-3)$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$f(x)=\sqrt{2 x}$$

Find a possible expression for a quadratic function \(f(x)\) having the given zeros. There can be more than one correct answer. \(x=-5\) is the only zero

Solve the inequality algebraically or graphically. $$x^{2}-4 \geq x$$

Solve the rational equation. Check your solutions. $$\frac{x}{2 x^{2}+x-3}+\frac{1}{x-1}=\frac{3}{2 x+3}$$

Use transformations to graph the quadratic function and find the vertex of the associated parabola. $$h(x)=-3(x+4)^{2}-2$$

Find the complex conjugate of each number. $$i-1$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$(g h)(-3)$$

Find a possible expression for a quadratic function \(f(x)\) having the given zeros. There can be more than one correct answer. $$x=\frac{1}{2} \text { and } x=3$$

Solve the inequality algebraically or graphically. $$x^{2}-9 \geq 2 x$$

Solve the rational equation. Check your solutions. $$\frac{x}{3 x^{2}+5 x-2}-\frac{5}{x+2}=\frac{-1}{3 x-1}$$

Use transformations to graph the quadratic function and find the vertex of the associated parabola. $$g(t)=2(t-3)^{2}+3$$

Find the complex conjugate of each number. $$-2 i+4$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$(g h)(0)$$

Find a possible expression for a quadratic function \(f(x)\) having the given zeros. There can be more than one correct answer. $$x=0.4 \text { and } x=0.8$$

Decide if each function is odd, even, or neither by using the definitions. $$f(x)=x+3$$

Solve the inequality algebraically or graphically. $$3 x^{2}-x-1 \geq 0$$

Solve the rational equation. Check your solutions. $$\frac{x-3}{2 x-4}+\frac{1}{x^{2}-4}=\frac{1}{x+2}$$

Write each quadratic function in the form \(f(x)=a(x-h)^{2}+k\) by completing the square. Also find the vertex of the associated parabola and determine whether it is a maximum or minimum point. $$g(x)=x^{2}+2 x+5$$

Find the complex conjugate of each number. $$3+\sqrt{2}$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$(f h)(-2)$$

Solve the quadratic equation by completing the square. $$x^{2}+4 x=-3$$

Decide if each function is odd, even, or neither by using the definitions. $$f(x)=-2 x$$