3. Functions

The green dotted line in the graph below represents the function $f\(\left\)(x\(\right\))$. The blue solid line represents the function $g\(\left\)(x\(\right\))$, which is the function $f\(\left\)(x\(\right\))$after it has gone through a shift transformation. Find the equation for $g\(\left\)(x\(\right\))$.

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

Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. ƒ(x)=x²+2

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

Begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. g(x) = 2√(x+1)-1

Use the graph of y = f(x) to graph each function g.

g(x) = f(x-1)+2

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. (5, -3)

Written below (green dotted curve) is a graph of the function $f\(\left\)(x\(\right\))=\(\sqrt{x-2}\)$.If g(x) (blue solid curve) is a reflection of f(x) about the y-axis what is the equation for g(x)?

Begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. g(x) = (x − 2)²

Begin by graphing the cube root function, f(x) = ∛x. Then use transformations of this graph to graph the given function. g(x) = (1/2)∛(x+2) - 2

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 $y=x^2$?

Use the graph of y = f(x) to graph each function g. g(x) = -f(x)+1