QuestionWhich intercepts will help you find the roots of the equation if $\sqrt{3 x+4}=-2$ ?
Select one: a. $x$ -intercepts of the graph of the function $y=\sqrt{3 x+4}-2$ b. $x$ -intercepts of the graph of the function $y=\sqrt{3 x+4}+2$ c. $y$ -intercepts of the graph of the function $y=\sqrt{3 x+4}-2$ d. $y$ -intercepts of the graph of the function $y=\sqrt{3 x+4}+2$

Studdy Solution

STEP 1

1. We are given the equation $\sqrt{3x+4} = -2$ .
2. We need to determine which intercepts will help find the roots of this equation.
3. The roots of the equation are the values of $x$ that satisfy the equation.

STEP 2

1. Analyze the given equation.
2. Understand the concept of intercepts.
3. Determine which intercepts are relevant for finding the roots.

STEP 3

Analyze the given equation $\sqrt{3x+4} = -2$ .
Note that the square root function $\sqrt{3x+4}$ is always non-negative for real numbers, meaning it cannot equal $-2$ . Therefore, there are no real solutions or roots for this equation.

STEP 4

Understand the concept of intercepts.
- The $x$ -intercepts of a graph are the points where the graph crosses the $x$ -axis, meaning the output $y = 0$ . - The $y$ -intercepts of a graph are the points where the graph crosses the $y$ -axis, meaning the input $x = 0$ .

STEP 5

Determine which intercepts are relevant for finding the roots.
Since we are looking for the roots of the equation $\sqrt{3x+4} = -2$ , we need to consider the $x$ -intercepts of the function related to this equation. However, since the equation has no real solutions, the graph of the function $y = \sqrt{3x+4} - 2$ will not cross the $x$ -axis, meaning it will have no $x$ -intercepts.
Therefore, the correct answer is: a. $x$ -intercepts of the graph of the function $y = \sqrt{3x+4} - 2$

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