8 a) y=x² stretched vertically by 8
That means (0,0) stays (0,0), and (1,1) becomes (1,8) and (-1,1) becomes (-1,8)
Answer: y = 8x²
8 b) y=x² compressed vertically by 1/5
Answer: y = (1/5) x²
9.
y = ax² + k through (-1,3) and (3,-13)
That means
3 = a (-1)² + k
-13 = a (3²) + k
Subtracting,
16 = a - 9a = -8a
a = -2
3 = -2 + k
k = 5
y = -2x² + 5
Check:
-2(-1)^2 + 5 = 3, good
-2(3)^2+5 = -18 + 5 = -13, good
Answer: a = -2, k = 5
Answer:
First we chose one side to solve.
I am doing the one on the left first.
so -3x+-24-12
-3x-12
Now we do the other side
62-24 is
38 therefore
-3x-12=38
Answer:
115
Step-by-step explanation:
You have to understand how piecewise functions first
I hope you do because I won't be explaining it here
1.
if it is continiuous at x=1 then the part of the function that approaches 1 from the left is the same value
so we have f(x)=3-x for x<1, so evaluate it for x=1,
we would get 3-1=2
so
if a=2 and b=3
f(x)=2x²+3x
for x=1, we get 2+3=5
it approaches 2 from the left but equals 5
2≠5
so it is not continuous because it doesn't approach the same value at x=1
2.
alright
so we established that it should approach 2 because we had the f(x)=3-x
so
f(1)=2=ax²+bx
2=a+b
the relationship is 2=a+b
3.
same as before, but use the other function, the one that is defined at x≥2
5x-10, 5(2)-10, 10-10, 0
it approaches 0
so
we must find one such that f(x)=0 for x=2 with the ax²+bx
0=a(2)²+b(2)
0=4a+2b
if we minus 2b both sides
-2b=4a
divide by 2
-b=2a
add b both sides
0=2a+b
4.
2=a+b
0=2a+b
2=a+b
minus b both sides
2-b=a
subsitute
0=2a+b
0=2(2-b)+b
0=4-2b+b
0=4-b
b=4
sub back
2-b=a
2-4=a
-2=a
a=-2
b=4
5.
graph f(x)=-2x²+4x from x=1 to x=2 and put a closed dot at (1,2) and an open dot at (2,0)
Answer: The price for the adult tickets is $12 and the price for the child ticket is $5.
Step-by-step explanation:
Let the price for the adult ticket be x
Let the price for the child ticket be y
According to question, On Friday ,
and on next day,
Now, we will use "Substitution Method" to solve the system of equations :
so, we will put the value of x in the first equation i.e.
Now, put the value of y in the equation that is given by
Hence, the price for the adult tickets is $12 and the price for the child ticket is $5.
