Do transformed functions of the form $f(x)=a \tan \left(\frac{1}{b} x\right)$ have the same behavior seen in the parent function, that is, f(-x)=-f(x) ? Justify your answer and how it helps to graph transformed functions.

In this exercise, g is related to one of the parent functions described in the earlier section. Describe the sequence of transformations from f to g.

$$g(x)=-\frac{1}{2} \sqrt{x+3}-1$$

Graph each logarithmic function. Compare each graph to the graph of its parent function. List each function's domain, range, y-intercept, and asymptotes. $y=\log _{3}(x-1)$

Use the description to write the square root function g.

The parent function $f(x)=\sqrt{x}$ is reflected across the y-axis, vertically stretched by a factor of 7 , and translated 3 units down.

In this exercise, g is related to one of the parent functions described in the earlier section. Use function notation to write g in terms of f.

$$g(x)=3+2(x-4)^2$$

Determine whether the statement given below is true or false and explain your answer.

The function $y=10^{(x-2)}$ has the same domain and range as the parent function $f(x)=10^x$.

g is related to one of the parent functions described in Section 1.6. Use function notation to write g in terms of f. g(x) = 2(x - 7)^2

Your friend says two different translations of the graph of the parent linear function can result in the graph of f(x) = x - 2. Is your friend correct? Explain.

g is related to a parent function f(x) = sin(x) or f(x) = cos(x). Use function notation to write g in terms of f. g(x) = 2 sin(4x - π) - 3

For each quadratic function, describe the transformation of its graph from the graph of the parent function $f(x) = x^2$. $y=\left(x-\frac{1}{2}\right)^{2}$

Identify each underlined word below by writing $A D J$ for adjective or $A D V$ for adverb on the line provided.

4. $\underline{\text{proud}}$ parent

Describe the transformations necessary to get from the graph of the parent function $f(x)=x^2$ to the graph of each of the given functions.

$$g(x)=5(x-6)^2+9$$

What transformations of the parent graph of $f(x)=\sqrt{x}$ produce the graphs of the following functions?
a. $m(x)=\sqrt{7 x-3.5}-10$ b. $j(x)=-2 \sqrt{12 x}+4$

h is related to one of the parent functions described in this chapter. Describe the sequence of transformations from f to h.

$$h(x) = 1/2(x - 1)^2 - 2$$