Question

from the parent functions f(x) = x. 3. f(x) = 5x + 2 4. f(x) 7. f(x) = \frac{1}{2}x - 7 8. f(x)

Explanation:

Step1: Analyze vertical stretch

The coefficient of $x$ in $f(x)=5x + 2$ is $5$. A non - unit coefficient of $x$ in a linear function $y = ax + b$ (compared to the parent function $y=x$) represents a vertical stretch. Here, the parent function $f(x)=x$ is vertically stretched by a factor of $5$.

Step2: Analyze vertical shift

The constant term in $f(x)=5x + 2$ is $2$. For a linear function of the form $y=ax + b$, the value of $b$ represents a vertical shift. So, the function is shifted up by $2$ units.

Answer:

The function $f(x)=5x + 2$ is obtained from the parent function $f(x)=x$ by a vertical stretch by a factor of $5$ and a vertical shift up by $2$ units.