We are asked to describe sequence of transformations used to produce the graph for each function.
First of all, let us understand transformation rules for functions.
Vertical Translation:
[tex]\begin{gathered} f(x)+d\Rightarrow\text{vertical translation up by d units} \\ f(x)-d\Rightarrow\text{vertical translation down by d units} \end{gathered}[/tex]Horizontal Translation:
[tex]\begin{gathered} f(x+c)\Rightarrow\text{horizontal translation left by c units} \\ f(x-c)\Rightarrow\text{horizontal translation right by c units} \end{gathered}[/tex]Reflection:
[tex]\begin{gathered} -f(x)\Rightarrow\text{ reflection over x-axis} \\ f(-x)\Rightarrow\text{ reflection over y-axis} \end{gathered}[/tex]Dilation:
[tex]\begin{gathered} a\cdot f(x)\Rightarrow\text{ vertical stretch for |}a|>1 \\ a\cdot f(x)\Rightarrow\text{ vertical compression for }0<|a|<1 \end{gathered}[/tex]Function 14:
[tex]y=-\sqrt[]{x+4}+1[/tex]As you can see,
it is reflected over the x-axis
(x+4) means translated left by 4 units
Also, +1 translated up by 1 unit
Function 15:
[tex]y=\frac{1}{4}|x+5|-4[/tex]As you can see,
It is vertically compressed by 1/4
(x+5) means translated left by 5 units
Also, -4 means translated down by 4 units
Function 16:
[tex]y=\sqrt[3]{-x}+5[/tex]As you can see,
it is reflected over the y-axis since f(-x)
+5 means translated up by 5 unit
Function 17:
[tex]y=-3(x+2)^2[/tex]As you can see,
it is reflected over the x-axis
(x+2) means translated left by 2 units
Also, It is vertically stretched by 3
Function 18:
[tex]y=\frac{1}{2}(x-4)^3-1[/tex]As you can see,
(x - 4) means translated right by 2 units
-1 means translated down by 1 unit
Also, It is vertically compressed by 1/2
