Question

graph the function
( h(x) = sqrt{x} - 5 )
choose the correct graph.
oa.
graph a
ob.
graph b
oc.
graph c
od.
graph d

Explanation:

Step1: Analyze the parent function

The parent function is \( y = \sqrt{x} \), which has a domain \( x \geq 0 \) and starts at the point \( (0,0) \), increasing slowly.

Step2: Determine the transformation

The given function is \( h(x)=\sqrt{x}-5 \). This is a vertical shift of the parent function \( y = \sqrt{x} \) down by 5 units. So the vertex (starting point) of \( h(x) \) will be at \( (0, 0 - 5)=(0,-5) \)? Wait, no, wait: Wait, the function is \( \sqrt{x}-5 \), so for the domain, the expression under the square root must be non - negative, so \( x\geq0 \). When \( x = 0 \), \( h(0)=\sqrt{0}-5=- 5 \). So the graph should start at \( (0,-5) \) and increase as \( x \) increases.

Now let's analyze the options:

• Option A: Let's check the starting point. If we look at the graph, we need to see the vertex. The function \( h(x)=\sqrt{x}-5 \) has vertex at \( (0, - 5) \) (since when \( x = 0 \), \( y=-5 \)) and domain \( x\geq0 \). Let's check the graphs. The graph of \( y = \sqrt{x}-5 \) should start at \( (0,-5) \) and increase. Let's check the options. The correct graph should have the curve starting at \( (0, - 5) \) (or \( x = 0,y=-5 \)) and increasing for \( x\geq0 \).

Wait, maybe I made a mistake earlier. Wait, the function is \( h(x)=\sqrt{x}-5 \), so the domain is \( x\geq0 \), and the range is \( y\geq - 5 \). So the graph should start at \( (0,-5) \) and go up as \( x \) increases. Let's check the options:

Looking at the options, let's assume that in option A, the graph starts at (0, - 5) and increases. Wait, maybe the original problem's options: Let's re - evaluate.

Wait, maybe I misread the function. Wait, the function is \( h(x)=\sqrt{x}-5 \), so when \( x = 0 \), \( y=-5 \); when \( x = 25 \), \( y=\sqrt{25}-5 = 5 - 5=0 \). So the graph passes through \( (25,0) \) and starts at \( (0,-5) \).

Now let's check the options:

Option A: Let's see the graph. If the graph has a starting point at \( (0,-5) \) and goes up, that would be the graph of \( y=\sqrt{x}-5 \).

Wait, maybe the correct option is A? Wait, no, wait. Wait, maybe I made a mistake. Wait, let's check again.

Wait, the parent function \( y = \sqrt{x} \) is shifted down by 5 units. So the vertex is at \( (0,-5) \), and the graph is increasing for \( x\geq0 \). So the correct graph should have the curve starting at \( (0, - 5) \) (or \( x = 0,y=-5 \)) and increasing as \( x \) increases.

So among the options, the graph that starts at \( (0,-5) \) (or near \( x = 0,y=-5 \)) and increases for \( x\geq0 \) is the correct one. Let's assume that option A is the correct one (since the other options may have different starting points or domains).

Answer:

The correct graph is the one that represents the function \( h(x)=\sqrt{x}-5 \), which starts at \( (0, - 5) \) and increases for \( x\geq0 \). If we assume the options are labeled A, B, C, D, and based on the analysis, the correct option is \(\boldsymbol{\text{Option A}}\) (assuming Option A has the curve starting at \( (0,-5) \) and increasing for \( x\geq0 \)).