Chapter 2

Solve the polynomial equation. In Exercises \(7-14,\) find all solutions. In Exercises \(15-18,\) find only real solutions. Check your solutions. $$2 x^{6}-7 x^{3}=7$$

Use the definition of i to solve the equation. $$-x^{2}=12$$

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. $$(f+g)(0)$$

This set of exercises will reinforce the skills illustrated in this section. Graph each pair of functions on the same set of coordinate axes, and find the domain and range of each function. $$f(x)=-(x-4)^{2}, g(x)=-(x+4)^{2}$$

Solve the quadratic equation by factoring. $$9 x^{2}+6 x+1=0$$

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

Solve the inequality by factoring. $$-3 x^{2}+x \leq-2$$

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

Use the definition of i to solve the equation. $$3 x^{2}=-30$$

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. $$(g+h)(0)$$

Factor to find the \(x\)-intercepts of the parabola described by the quadratic function. Also find the real zeros of the function. $$g(x)=x^{2}-9$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$H(s)=-|s|-3$$

Solve the inequality by factoring. $$6 x^{2}-5 x<6$$

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

Use the definition of i to solve the equation. $$5 x^{2}=-60$$

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. $$(g+h)(1)$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$F(x)=-\sqrt{x+4}$$

Factor to find the \(x\)-intercepts of the parabola described by the quadratic function. Also find the real zeros of the function. $$f(t)=-t^{2}+4 t$$

Solve the inequality by factoring. $$2 x^{2}

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

Find the real and imaginary parts of the complex number. 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. $$(f+h)(-2)$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$h(x)=-\frac{1}{2}|x+1|-3$$

Factor to find the \(x\)-intercepts of the parabola described by the quadratic function. Also find the real zeros of the function. $$h(s)=-s^{2}+2 s-1$$

Solve the inequality by factoring. $$6 x^{2} \geq 13 x-5$$

Solve the rational equation. Check your solutions. $$\frac{1}{2 x}+\frac{4}{5}=\frac{3}{x}$$

Find the real and imaginary parts of the complex number. $$-3$$

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. $$(f+h)(0)$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$h(x)=-2|x-4|+1$$

Factor to find the \(x\)-intercepts of the parabola described by the quadratic function. Also find the real zeros of the function. $$f(x)=x^{2}+4 x+4$$

Solve the inequality by factoring. $$5 x^{2}-8 x \geq 4$$

Solve the rational equation. Check your solutions. $$\frac{1}{x^{2}}-\frac{3}{x}=10$$

Find the real and imaginary parts of the complex number. $$-\pi i$$

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. $$(f-g)(2)$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$g(x)=-3(x+2)^{2}-4$$

Factor to find the \(x\)-intercepts of the parabola described by the quadratic function. Also find the real zeros of the function. $$g(x)=2 x^{2}+5 x-3$$

Solve the inequality by factoring. $$-3 x^{2} \leq-7 x-6$$

Solve the rational equation. Check your solutions. $$\frac{1}{x^{2}}-\frac{7}{x}=18$$

Find the real and imaginary parts of the complex number. $$i \sqrt{3}$$

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. $$h(x)=-\frac{1}{3}(x-2)^{2}-\frac{3}{2}$$

Factor to find the \(x\)-intercepts of the parabola described by the quadratic function. Also find the real zeros of the function. $$f(x)=6 x^{2}-x-2$$

Solve the inequality by factoring. $$10 x^{2} \leq-13 x+3$$

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

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. $$(g-h)(-2)$$

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

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

Solve the inequality by factoring. $$12 x^{2}+5 x-2 \geq 0$$

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

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. $$(g-h)(3)$$