enter the correct answer in the box.\nthe graph of function g is created by applying these transformations…
enter the correct answer in the box.\nthe graph of function g is created by applying these transformations to the parent tangent function:\n- reflection over the x - axis\n- horizontal stretch by a factor of 5\n- vertical shift down 3 units\nwrite the equation representing function g.\ng(x) =
Answer
Explanation:
Step1: Start with parent tangent function
The parent tangent function is $y = \tan(x)$.
Step2: Apply reflection over x - axis
When a function $y = f(x)$ is reflected over the $x$-axis, the new function is $y=-f(x)$. So, we get $y = -\tan(x)$.
Step3: Apply horizontal stretch
For a horizontal stretch of a function $y = f(x)$ by a factor of $a$, the new function is $y = f(\frac{x}{a})$. Here $a = 5$, so we have $y=-\tan(\frac{x}{5})$.
Step4: Apply vertical shift
When a function $y = f(x)$ is shifted down by $b$ units, the new function is $y=f(x)-b$. Here $b = 3$, so $g(x)=-\tan(\frac{x}{5})-3$.
Answer:
$-\tan(\frac{x}{5})-3$