Question

the function g(x)=3.9\sqrt{x}+6.2 models the median height, g(x), in inches, of children who are x months of age. the graph of g is shown.
a. describe how the graph can be obtained using transformations of the square - root function f(x)=\sqrt{x}.
a. shrink f(x) horizontally by a factor of 3.9. shift f(x) left by 6.2 units.
b. stretch f(x) vertically by a factor of 3.9. shift f(x) up by 6.2 units.
c. stretch f(x) vertically by a factor of 3.9. shift f(x) right by 6.2 units.
d. shrink f(x) vertically by a factor of 3.9. shift f(x) up by 6.2 units.

Explanation:

Step1: Recall function - transformation rules

For a function $y = af(x)$ where $a>1$, it is a vertical stretch of $y = f(x)$ by a factor of $a$. For $g(x)=3.9\sqrt{x}+6.2$ compared to $f(x)=\sqrt{x}$, the coefficient 3.9 in front of $\sqrt{x}$ indicates a vertical - stretch.

Step2: Recall vertical - shift rules

For a function $y = f(x)+k$ where $k > 0$, it is a vertical shift of $y = f(x)$ up by $k$ units. In $g(x)=3.9\sqrt{x}+6.2$, the + 6.2 indicates a vertical shift up by 6.2 units.

Answer:

B. Stretch f(x) vertically by a factor of 3.9. Shift f(x) up by 6.2 units.