Question

Which key features can you identify from the following equation? Provide enough information to describe the appearance and behavior of the graph.

f(x)= -6 Radical x-4 + 8 ( + 8 is on outside of radical )

I know the 8 is the y-intercept but got confused on how to describe the function

Answer 1

Given the function $f(x)=-6\sqrt{x-4}+8.$

1. The domain of the function (possible values for x) is:

$x-4\ge 0,\\ \\x\ge 4.$

2. The range of the function (possible values for y) is:

$y=f(x)\le 8.$

3. x-intercept is when y=0, then

$0=-6\sqrt{x-4}+8,\\ \\\sqrt{x-4}=\dfrac{8}{6}=\dfrac{4}{3},\\ \\x-4=\dfrac{16}{9},\\ \\x=4+\dfrac{16}{9}=\dfrac{52}{9}\approx 5.778.$

Therefore, x-intercept is at point $\left(5\frac{7}{9},0\right).$

4. There are no y-intercepts.

5. The graph of the function is decreasing (see attached diagram)

Answer 2

Plato Answer:The equation reveals that the vertex, or starting point, of this square root function is at (4,8). Because the domain is x ≥ 4, the graph is defined only for x-values to the right of (4,8). To the left of (4,8), the graph is undefined. The coefficient of -6 means the graph will change at a faster rate than the parent graph. The negative sign indicates the function is decreasing on its domain—as x approaches positive infinity, f(x) approaches negative infinity.

Step-by-step explanation: