a)The graph of the equation $f(x)=sqrt{x-1}+2$ is the graph of a upper half-parabola that opens right and has its vertex at (1, 2).

Domain= $left{ xin R| xgeq1right}$

Range=$left{ yin R| ygeq0right}$

b) The graph of the equation $f(x)=|x-1|+2$ is the graph of a V-shape, that opens up and has it’s vertex at (1, 2).

Domain= $left{ xin R right}$

Range=$left{ yin R| ygeq0right}$

c) The graph of the equation $f(x)=dfrac{1}{x-1}+2$ is the graph of a hyperbola,that has asymptotes $y=2$ and $x=1$.

Domain= $left{ xin R| xne1 right}$

Range=$left{ yin R| yne2right}$

a) upper-half of the parabola that opens to the right with vertex at $(1,2)$

b) V-shaped that opens upward with vertex at $(1,2)$

c) Hyperbola with asymptotes at $x=1$ and $y=2$

a)The graph of $y=sqrt{x}$ is upper half and the graph of $y=-sqrt{x}$ lower half of parabola opening right

b)The graph of $y=|x|$ opens up and the graph of $y=-|x|$ opens down.

c) Graph of $y=dfrac{1}{x}$ lies to lower left and upper right of asymptotes $x=0$ and graph of $y=-dfrac{1}{x}$ lies to upper left and lower right of asymptotes $x=0$

a) The graph of $y=sqrt{x}$ is the upper half and the graph of $y=-sqrt{x}$ is the lower half of parabola opening right.

b) The graph of $y=|x|$ opens up and the graph of $y=-|x|$ opens down.

c) The graph of $y=dfrac{1}{x}$ lies to the lower left and upper right of asymptotes $x=0$ and the graph of $y=-dfrac{1}{x}$ lies to the upper left and lower right of asymptotes $x=0$

a)The graph of $y=2sqrt{x}$ is narrower than the graph of $y=sqrt{x}$

b) The graph of $y=2|x|$ is narrower than the graph of $y=|x|$

c) The graph of $y=dfrac{2}{x}$ is narrower than the graph of $y=dfrac{1}{x}$

a) The graph of $y=2sqrt{x}$ is narrower than the graph of $y=sqrt{x}$

b) The graph of $y=2|x|$ is narrower than the graph of $y=|x|$

c) The graph of $y=dfrac{2}{x}$ is narrower than the graph of $y=dfrac{1}{x}$

The function $y=x^{3}$ is a cubic function, and is the parent graph for all other cubic functions.

The function $y=x^{2}$ is a quadratic function, and is the parent graph for all other quadratic functions

Examples:

The function $y=x^3$ is a cubic function and is the parent graph for all other cubic functions

The function $y=x^2$ is a quadratic function and is the parent graph for all other quadratic functions