Chapter 2

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(g \circ h)(-12)$$

Use a graphing utility to find all real solutions. You may need to adjust the window size manually or use the ZOOMFIT feature to get a clear graph. $$\text { Solve } \sqrt{x-1.95}-3.6=-2.5$$

Compute the zeros of the quadratic function. $$f(x)=2 x^{2}-x+8$$

Use a graphing utility to decide if the function is odd, even, or neither. $$f(x)=x^{2}-4 x+1$$

Solve the quadratic equation using any method. Find only real solutions. $$x^{2}-9=0$$

Find the vertex and axis of symmetry of the associated parabola for each quadratic function. Sketch the parabola. Find the intervals on which the function is increasing and decreasing, and find the range. $$h(x)=\frac{1}{4} x^{2}+\frac{1}{2} x-2$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(f \circ g)(4)$$

Use a graphing utility to find all real solutions. You may need to adjust the window size manually or use the ZOOMFIT feature to get a clear graph. $$\text { Solve } \sqrt{0.3 x+0.95}-\sqrt{0.75 x-0.5}=-0.3$$

Compute the zeros of the quadratic function. $$f(x)=-2 x^{2}-2 x+11$$

Use a graphing utility to decide if the function is odd, even, or neither. $$f(x)=-2 x^{2}+2 x+3$$

Solve the quadratic equation using any method. Find only real solutions. $$-x^{2}+2 x=1$$

Find the vertex and axis of symmetry of the associated parabola for each quadratic function. Sketch the parabola. Find the intervals on which the function is increasing and decreasing, and find the range. $$g(x)=-\frac{1}{6} x^{2}+\frac{1}{3} x+1$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(f \circ g)(9)$$

Use a graphing utility to find all real solutions. You may need to adjust the window size manually or use the ZOOMFIT feature to get a clear graph. $$\text { Solve } \sqrt{0.3 x+0.95}-\sqrt{0.75 x-0.5}=-0.3$$

Compute the zeros of the quadratic function. $$g(t)=-5 t^{2}+2 t-3$$

Solve the quadratic equation using any method. Find only real solutions. $$x^{2}-4 x=-4$$

Use a graphing utility to decide if the function is odd, even, or neither. $$f(x)=2 x^{3}-x$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(g \circ f)(2)$$

Use a graphing utility to find all real solutions. You may need to adjust the window size manually or use the ZOOMFIT feature to get a clear graph. Graphically solve \(\sqrt{x+1}=x+k\) for \(k=\frac{1}{2}, 1,\) and 2 How many solutions does the equation have for each value of \(k ?\)

Compute the zeros of the quadratic function. $$h(x)=3 x^{2}+8 x-16$$

Use a graphing utility to decide if the function is odd, even, or neither. $$f(x)=(x+1)(x-2)(x+3)$$

Solve the quadratic equation using any method. Find only real solutions. $$-2 x^{2}-1=3 x$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(g \circ f)(1)$$

Use a graphing utility to find all real solutions. You may need to adjust the window size manually or use the ZOOMFIT feature to get a clear graph. Graphically solve \(\sqrt{x-k}=x\) for \(k=-2,0,\) and 2 How many solutions does the equation have for each value of \(k ?\)

Compute the zeros of the quadratic function. $$f(t)=2 t^{2}+11 t+9$$

Use a graphing utility to decide if the function is odd, even, or neither. $$f(x)=x^{4}-5 x^{2}+4$$

Solve the quadratic equation using any method. Find only real solutions. $$-3 x^{2}-2=7 x$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(g \circ f)(-3)$$

In this set of exercises you will use radical and rational equations to study real-world problems. Four students plan to rent a minivan for a weekend trip and share equally in the rental cost of the van. By adding two more people, each person can save \(\$ 10\) on his or her share of the cost. How much is the total rental cost of the van?

Find all solutions of the quadratic equation. Relate the solutions of the equation to the zeros of an appropriate quadratic function. $$x^{2}+2 x+3=0$$

Solve the quadratic equation using any method. Find only real solutions. $$x^{2}-2 x=9$$

Use a graphing utility to decide if the function is odd, even, or neither. $$f(x)=-x^{4}+4 x^{2}$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(g \circ f)(-5)$$

In this set of exercises you will use radical and rational equations to study real-world problems. Two painters are available to paint a room. Working alone, the first painter can paint the room in 5 hours. The second painter can paint the room in 4 hours working by herself. If they work together, they can paint the room in \(t\) hours. To find \(t\), we note that in 1 hour, the first painter paints \(\frac{1}{5}\) of the room and the second painter paints \(\frac{1}{4}\) of the room. If they work together, they paint \(\frac{1}{t}\) portion of the room. The equation is thus $$\frac{1}{5}+\frac{1}{4}=\frac{1}{t}$$. Find \(t,\) the time it takes both painters to paint the room working together.

Find all solutions of the quadratic equation. Relate the solutions of the equation to the zeros of an appropriate quadratic function. $$-x^{2}+x-5=0$$

Solve the quadratic equation using any method. Find only real solutions. $$-x^{2}-3 x=1$$

Applications In this set of exercises, you will use properties of functions to study real-world problems. Demand Function The demand for a product, in thousands of units, is given by \(d(x)=\frac{100}{x},\) where \(x\) is the price of the product, \((x>0) .\) Is this an increasing or a decreasing function? Explain.

Graph each quadratic function by finding a suitable viewing window with the help of the TABLE feature of a graphing utility. Also find the vertex of the associated parabola using the graphing utility. $$y_{1}(x)=0.4 x^{2}+20$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(h \circ f)(2)$$

In this set of exercises you will use radical and rational equations to study real-world problems. Two water pumps work together to fill a storage tank. If the first pump can fill the tank in 6 hours and the two pumps working together can fill the tank in 4 hours, how long would it take to fill the storage tank using just the second pump?

Find all solutions of the quadratic equation. Relate the solutions of the equation to the zeros of an appropriate quadratic function. $$-3 x^{2}+2 x-4=0$$

Solve the quadratic equation using any method. Find only real solutions. $$(x-1)(x+2)=1$$

Applications In this set of exercises, you will use properties of functions to study real-world problems. Revenue The revenue for a company is given by \(R(x)=30 x\) where \(x\) is the number of units sold in thousands. Is this an increasing or a decreasing function? Explain.

Graph each quadratic function by finding a suitable viewing window with the help of the TABLE feature of a graphing utility. Also find the vertex of the associated parabola using the graphing utility. $$g(s)=-s^{2}-15$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(h \circ f)(-3)$$

Find all solutions of the quadratic equation. Relate the solutions of the equation to the zeros of an appropriate quadratic function. $$-2 x^{2}+3 x-1=0$$

Solve the quadratic equation using any method. Find only real solutions. $$(x+1)(x-2)=2$$

Applications In this set of exercises, you will use properties of functions to study real-world problems. Depreciation The value of a computer \(t\) years after purchase is given by \(v(t)=2000-300 t,\) where \(v(t)\) is in dollars. Find the average rate of change of the value of the computer on the interval [0,3] , and interpret it.

Graph each quadratic function by finding a suitable viewing window with the help of the TABLE feature of a graphing utility. Also find the vertex of the associated parabola using the graphing utility. $$h(x)=(\sqrt{2}) x^{2}+x+1$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(h \circ f)\left(\frac{1}{2}\right)$$