Answer:
- vertical scaling by a factor of 1/3 (compression)
- reflection over the y-axis
- horizontal scaling by a factor of 3 (expansion)
- translation left 1 unit
- translation up 3 units
Step-by-step explanation:
These are the transformations of interest:
g(x) = k·f(x) . . . . . vertical scaling (expansion) by a factor of k
g(x) = f(x) +k . . . . vertical translation by k units (upward)
g(x) = f(x/k) . . . . . horizontal expansion by a factor of k. When k < 0, the function is also reflected over the y-axis
g(x) = f(x-k) . . . . . horizontal translation to the right by k units
__
Here, we have ...
g(x) = 1/3f(-1/3(x+1)) +3
The vertical and horizontal transformations can be applied in either order, since neither affects the other. If we work left-to-right through the expression for g(x), we can see these transformations have been applied:
- vertical scaling by a factor of 1/3 (compression) . . . 1/3f(x)
- reflection over the y-axis . . . 1/3f(-x)
- horizontal scaling by a factor of 3 (expansion) . . . 1/3f(-1/3x)
- translation left 1 unit . . . 1/3f(-1/3(x+1))
- translation up 3 units . . . 1/3f(-1/3(x+1)) +3
_____
<em>Additional comment</em>
The "working" is a matter of matching the form of g(x) to the forms of the different transformations. It is a pattern-matching problem.
The horizontal transformations could also be described as ...
- translation right 1/3 unit . . . f(x -1/3)
- reflection over y and expansion by a factor of 3 . . . f(-1/3x -1/3)
The initial translation in this scenario would be reflected to a translation left 1/3 unit, then the horizontal expansion would turn that into a translation left 1 unit, as described above. Order matters.
Answer: 1 and 2
Step-by-step explanation: 1 and 2 because if you are graphing this the formula to find the slope / the line is y = x + some number. In the formula x is how much the line goes from the x axis and the number is how much it is from the y axis. On #2 the problem is 3y = 2x + 4 so to follow the formula you need to divide both sides by 3 to get y = 2/3x + 4. For #3 you do the same thing to get y = -3/2x -5. Finally for #1 the equation is 2x + 3y = 7 so to get the slope / line you need to put x on the other side so now it is 3y = 7-2x then you divide both sides by 3 and get y = -2/3x + 7 and on 1 and 2 there x is 2/3 (the negative doesn't matter and the random number) so they are parallel.
Answer:
Yes
Step-by-step explanation:
Graphs are functions when there is only one output for every input. In other words, for every "x" value, there must be only "y" value. This graph depicts a function because it abides by this rule. To be exact, this is an exponential function with the formula: f(x) = (x + 2)².

The coefficient is a number before a variable.
Here, the coefficient is 9.
The like terms are any terms that have the same variable.
Here, 9k and -k are like terms, and 7 and 4 are like terms as well.
Combine like terms:
8k+3
The constants are: 7 and 4 (Constants are numbers in an expression or equation)
After combining like terms, the constant became
3


Minimum is (5,0)
There is no maximum so maximum is N/A
Where the function is increasing is x>5
Function decreases where x<5