Question

Which statements describe the graph of y = Negative RootIndex 3 StartRoot x minus 1 EndRoot + 2? Select three options. The graph has a domain of all real numbers. The graph has a range of y greater-than-or-equal-to 1. As x is increasing, y is decreasing. The graph has a y-intercept at (0, 1). The graph has an x-intercept at (–7, 0).

Answer 1

As x is increasing, y is decreasing.

Step-by-step explanation:

Given function,

$y=-\sqrt{3x-1}+2$,

The function is defined if,

$3x-1\geq 0$

$3x \geq 1$

$\implies x \geq \frac{1}{3}$,

That is, y is defined for all real values greater than or equal to 1/3.

Thus, Domain = All real numbers greater or equal to 1.

if x = 1/3

$y=2$

Or for x > 1/3 ⇒ y < 2

So, the possible value of y is less than or equal to 2.

i.e. Range = all real numbers less than or equal to 2.

∵ $x\rightarrow \infty\implies y\rightarrow -\infty$

Thus, As x is increasing, y is decreasing.

If x= 0 ⇒ y = not defined.

⇒ The graph has no y-intercept.

If y = 0,

$0=-\sqrt{3x-1}+2$

$\sqrt{3x-1}=2$

$3x-1=4$

$3x=5$

$\implies x =\frac{5}{3}$

i.e., the graph has an x-intercept at (5/3, 0).

#Learn more:

Find domain and range :

https://brainly.in/question/4345343