Which of the following describes the transformation of g (x) = 3 (2) Superscript negative x Baseline + 2 from the parent functio
n f (x) = 2 Superscript x?
reflect across the x-axis, stretch the graph vertically by a factor of 3, shift 2 units up
reflect across the y-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the x-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up
reflect across the x-axis, stretch the graph vertically by a factor of 3, shift 2 units up
reflect across the y-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the x-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up
2 answers:
Option d: reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.
Step-by-step explanation:
The parent function is
The transformation function is
In the transformed function, the function is added +2, which shifts the graph by 2 units up.
Also, the function is multiplied by 3, which stretches the function vertically by a factor of 3 units.
The variable x is multiplied by -1, such that the function reflects across y-axis.
Thus, the correct answer is option d.
The graph is attached below which shows the parent function and the transformed function.
The transformation function is reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.
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Answer:
the 8% loan has a principal of $37500
the 12% loan has a principal of $12500
Step-by-step explanation:
Let's start by writing the general equation for the interest hwre I is the interest, P is the principal (in our case would be loan amounts), "r" is the interest rate in decimal form (in our case one would be 0.12, and the other one 0.08), and t is the time in years (in our case 1 year).
Then we write the interest equation coming from each loan at the end of this year (we call I1 the interest coming from the 12% loan and I2 the interest coming from the 8% one). Since we don't know the loan amounts (in fact those are what we need to find) we will name one "x" and the other "y":
Next, we add these last two equations term by term, and replace the addition of both interests by $4500 as given in the information:
This is our first equation in the variables x and y which are our unknowns.
Now we generate the second equation on x and y by writing in agebraic terms the other piece of information we have: "the total of the two loans is $50000. That is the addition of the principals x and y should equal $50000:
We solve for y in this last equation and replace its form in terms of x in the equation of the interest, and solve for the unknown x:
Therefore the amount of the loan at 12% is $12500
Now to find the amount of the second loan "y" we use the equation for the totals of the loans:
Therefore, the loan at 8% is $37500