Answer:
x = -1
Step-by-step explanation:
With the axis of symmetry, think of it as where you would slice this line in half, and both sides would look identical to each other. Since this is a quadratic function, this would be at where the vertex is.
The vertex is the part of the line where it "turns" around and starts going the other way. So vertex of this line is at (-1, 3).
Therefore, the axis of symmetry is at x = -1. This is since the function is pointing either up/down, and any value that is x = _ is a vertical line.
Using function concepts, it is found that:
- a) The y-intercept is y = 2.5.
- b) The horizontal asymptote is x = 3.
- c) The function is decreasing.
- d) The domain is
and the range is 
. - e) The graph is given at the end of the answer.
------------------------------------
The given function is:
------------------------------------
Question a:
The y-intercept is g(0), thus:
The y-intercept is y = 2.5.
------------------------------------
Question b:
The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.
--------------------------------------------------
Thus, the horizontal asymptote is x = 3.
--------------------------------------------------
Question c:
The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.
--------------------------------------------------
Question d:
- Exponential function has no restrictions in the domain, so it is all real values, that is .
- From the limits in item c, the range is:
--------------------------------------------------
The sketching of the graph is given appended at the end of this answer.
A similar problem is given at brainly.com/question/16533631
Answer:
A
Step-by-step explanation:
The line cuts the y at positive two. The rise over run of the slope is -3/1, or 3.
Just had a test on these kinds of problems and i got 100.
Answer:
y = x + 1
Step-by-step explanation:
The gradient of a line can be defined by the equation:
m (gradient) = (y1 – y2 ) ÷ (x1 – x2) ----> "1" and "2" should be in subscript
For (-7,-6) we use x2 and y2 (because this point can be anywhere along a line):
x2 = -7, y2 = -6
Plug these values into the formula above:
m = (y-(-6)) ÷ (x-(-7))
m = (y+6) ÷ (x+7)
At this stage, the equation can't be solved as there are two unknowns. Therefore, the gradient must be found another way. Two lines are parallel if they have the same gradient - in their y=mx+c equations, m will be equal.
x - y=7 is the line alluded to in the question. Rearranging this equation into the line equation format gives:
y = x-7 ---> The gradient (coefficient of x) is 1.
Therefore, the gradient of the other parallel line must also be 1.
This can be substituted into the previous equation to give:
1 = (y+6)÷(x+7)
x+7 = y+6
x+1 = y
Therefore, the answer is y=x+1
A: 3
Good luck on everything
