The domain of the function is x>=-7.
This is because the expression inside the square root, 6x+42, must be non-negative for real values of y to exist.
Setting 6x+42>=0 and solving for x, we get x>=-7. Therefore, the domain of the function is x>=-7.
What is the domain of the function y=3 sq root 6x+42 ?
x>=0
x<=7
x>=-6
x>=-7
5 answers
2. What are the domain and range of the function (Image: y equals 2 start root 3x plus 4 end root minus 5)? (1 point)
(Image: lower x greater-than-or-equal-to negative four-thirds semi-colon lower y greater-than-or-equal-to negative 5)
(Image: lower x greater-than-or-equal-to four-thirds semi-colon lower y greater-than-or-equal-to negative 5)
(Image: lower x less-than-or-equal-to negative four-thirds semi-colon lower y less-than-or-equal-to negative 5)
(Image: lower x great-than-or-equal-to negative four-thirds semi-colon lower y greater-than-or-equal-to 5)
(Image: lower x greater-than-or-equal-to negative four-thirds semi-colon lower y greater-than-or-equal-to negative 5)
(Image: lower x greater-than-or-equal-to four-thirds semi-colon lower y greater-than-or-equal-to negative 5)
(Image: lower x less-than-or-equal-to negative four-thirds semi-colon lower y less-than-or-equal-to negative 5)
(Image: lower x great-than-or-equal-to negative four-thirds semi-colon lower y greater-than-or-equal-to 5)
The domain of the function is x >= -4/3.
To find the domain, we need to consider the expression inside the square root, 3x + 4. For real values of y to exist, 3x + 4 must be non-negative (or equal to zero) so that we do not take the square root of a negative number. Solving 3x + 4 >= 0, we get x >= -4/3.
The range of the function is y >= -5.
To see this, note that the square root term is always non-negative since we only deal with the positive square root. Therefore, the minimum value of y occurs when the expression inside the square root is zero, which occurs when 3x + 4 = 0, or x = -4/3. Evaluating the function at this point, we get y = -5. Since y is always greater than or equal to -5 (but can be greater when x is larger), the range of the function is y >= -5.
To find the domain, we need to consider the expression inside the square root, 3x + 4. For real values of y to exist, 3x + 4 must be non-negative (or equal to zero) so that we do not take the square root of a negative number. Solving 3x + 4 >= 0, we get x >= -4/3.
The range of the function is y >= -5.
To see this, note that the square root term is always non-negative since we only deal with the positive square root. Therefore, the minimum value of y occurs when the expression inside the square root is zero, which occurs when 3x + 4 = 0, or x = -4/3. Evaluating the function at this point, we get y = -5. Since y is always greater than or equal to -5 (but can be greater when x is larger), the range of the function is y >= -5.
3. Which of the following is a graph of the equation (Image: y equals StartRoot x plus 5 EndRoot minus 2)?
(Image: The graph shows the equation y equals StartRoot x EndRoot translated 5 units to the left and 2 units down.)
(Image: The graph shows the equation y equals StartRoot x EndRoot translated 5 units to the left and 2 units up.)
(Image: The graph shows the equation y equals StartRoot x EndRoot translated 5 units to the right and 2 units up.)
(Image: The graph shows the equation y equals StartRoot x EndRoot translated 5 units to the right and 2 units down.)
(Image: The graph shows the equation y equals StartRoot x EndRoot translated 5 units to the left and 2 units down.)
(Image: The graph shows the equation y equals StartRoot x EndRoot translated 5 units to the left and 2 units up.)
(Image: The graph shows the equation y equals StartRoot x EndRoot translated 5 units to the right and 2 units up.)
(Image: The graph shows the equation y equals StartRoot x EndRoot translated 5 units to the right and 2 units down.)
The graph that shows the equation y equals StartRoot x plus 5 EndRoot minus 2 is:
(Image: The graph shows the equation y equals StartRoot x EndRoot translated 5 units to the left and 2 units down.)
To obtain this graph, we start with the graph of y = sqrt(x), which is a curve that starts at the origin and moves upwards and to the right. To obtain y = sqrt(x + 5) - 2, we first shift the graph 5 units to the left by replacing x with (x + 5), as follows: y = sqrt(x + 5). This moves the graph to the left by 5 units. Then, we shift the graph down 2 units by subtracting 2 from the equation: y = sqrt(x + 5) - 2. This moves the graph down by 2 units. The resulting curve has its vertex at (-5, -2) and moves upwards and to the right.
(Image: The graph shows the equation y equals StartRoot x EndRoot translated 5 units to the left and 2 units down.)
To obtain this graph, we start with the graph of y = sqrt(x), which is a curve that starts at the origin and moves upwards and to the right. To obtain y = sqrt(x + 5) - 2, we first shift the graph 5 units to the left by replacing x with (x + 5), as follows: y = sqrt(x + 5). This moves the graph to the left by 5 units. Then, we shift the graph down 2 units by subtracting 2 from the equation: y = sqrt(x + 5) - 2. This moves the graph down by 2 units. The resulting curve has its vertex at (-5, -2) and moves upwards and to the right.