Graph each function.

$\text{ƒ}\left(x\right)=-\text{√}x-2$

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=-6x+9,g\left(x\right)=5x+7$

Given functions f and g, (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=-6x+9,g\left(x\right)=5x+7$

Graph each function. ƒ(x) = 2∛(x+1)-2

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=8x+12,g\left(x\right)=3x-1$

Given functions f and g, find (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=8x+12,g\left(x\right)=3x-1$

If three distinct points A, B, and C in a plane are such that the slopes of nonvertical line segments AB, AC, and BC are equal, then A, B, and C are collinear. Otherwise, they are not. Use this fact to determine whether the three points given are collinear. (-1, 4), (-2, -1), (1, 14)

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

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\text{√}x,g\left(x\right)=x+3$

Given functions f and g, find (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\text{√}x,g\left(x\right)=x+3$

Given functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. ƒ(x)=√x, g(x)=x-1

Consider the following nonlinear system. Work Exercises 75 –80 in order.

$y=\mid x-1\mid$

$y=x^2-4$

How is the graph of y = x^2 - 4 obtained by transforming the graph of $y=x^2$?

If three distinct points A, B, and C in a plane are such that the slopes of nonvertical line segments AB, AC, and BC are equal, then A, B, and C are collinear. Otherwise, they are not. Use this fact to determine whether the three points given are collinear. (-1, -3), (-5, 12), (1, -11)

Graph each function.

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=x^3,g\left(x\right)=x^2+3x-1$

Given functions f and g, (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=x^3,g\left(x\right)=x^2+3x-1$

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=x+2,g\left(x\right)=x^4+x^2-4$

An equation that defines y as a function of x is given. Find ƒ(3). x-4y=8

Given functions f and g, find (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=x+2,g\left(x\right)=x^4+x^2-4$

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\text{√}(x-1),g\left(x\right)=3x$

An equation that defines y as a function of x is given. Find ƒ(3). y+2x²=3-x

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\text{√}(x-1),g\left(x\right)=3x$

Given functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. ƒ(x)=√(x-2), g(x)=2x

Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. ƒ(x)=-3(x-2)²+1

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\frac{2}{x},g\left(x\right)=x+1$

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\frac{2}{x},g\left(x\right)=x+1$

Given functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\frac{4}{x},g\left(x\right)=x+4$

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\surd (x+2),g\left(x\right)=-\left(\frac{1}{x}\right)$

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\surd (x+2),g\left(x\right)=-\left(\frac{1}{x}\right)$

Given functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\surd (x+4),g\left(x\right)=-\left(\frac{2}{x}\right)$