Graph each function. See Examples 1 and 2. g(x)=(1/2)x²

Graph each function. See Examples 1 and 2. ƒ(x)=-(1/2)x²

Graph each function. See Examples 1 and 2. ƒ(x)=-3|x|

Graph each function. See Examples 1 and 2. h(x)=√(4x)

Graph each function. See Examples 1 and 2. ƒ(x)=-√-x

Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis, (b) y-axis, and (c) origin. (-4, -2)

The graph of y=|x-2| is symmetric with respect to a vertical line. What is the equation of that line?

Without graphing, determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. See Examples 3 and 4. y=x²+5

Without graphing, determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. See Examples 3 and 4. x²+y²=12

Determine whether each function is even, odd, or neither. ƒ(x)=-x³+2x

Determine whether each function is even, odd, or neither. ƒ(x)=x⁵-2x³

Determine whether each function is even, odd, or neither. ƒ(x)=0.5x⁴-2x²+6

Determine whether each function is even, odd, or neither. ƒ(x)=x³-x+9

Determine whether each function is even, odd, or neither. ƒ(x)=x⁴-5x+8

Determine whether each function is even, odd, or neither. ƒ(x)=x+1/x⁵

Determine whether each function is even, odd, or neither. ƒ(x)=x⁴+4/x²

Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. g(x)=(x+2)²

Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. h(x)=-(x+1)³

Each of the following graphs is obtained from the graph of ƒ(x)=|x| or g(x)=√x by applying several of the transformations discussed in this section. Describe the transformations and give an equation for the graph.

Each of the following graphs is obtained from the graph of ƒ(x)=|x| or g(x)=√x by applying several of the transformations discussed in this section. Describe the transformations and give an equation for the graph.

Let ƒ(x)=x²+3 and g(x)=-2x+6. Find each of the following. (ƒ+g)(3)

Let ƒ(x)=x²+3 and g(x)=-2x+6. Find each of the following. (ƒ-g)(-1)

Let ƒ(x)=x²+3 and g(x)=-2x+6. Find each of the following. (ƒg)(4)

Let ƒ(x)=x²+3 and g(x)=-2x+6. Find each of the following. (ƒ/g)(-1)

For the pair of functions defined, find (ƒ+g)(x), (ƒ-g)(x), (ƒg)(x), and (f/g)(x).Give the domain of each. ƒ(x)=4x²+2x, g(x)=x²-3x+2

For the pair of functions defined, find (ƒ+g)(x), (ƒ-g)(x), (ƒg)(x), and (f/g)(x).Give the domain of each. ƒ(x)=√(5x-4), g(x)=-(1/x)

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=2-x

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=1-x

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=6x+2

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=-2x+5