Question

Will someone PLEASE check my answers asap?? will mark a brainliest!!


1) The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)^x − k. If g(x) is obtained by shifting f(x) down by 3 units, the value of k is ____


2) Find an equivalent function to f(x) = 4(7)2x.

A) f(x) = 282x
B) f(x) = 4(49)x
C) f(x) = 196x
D) f(x) = 16x(49)x



3) The functions f(x) and g(x) are described using the following equation and table:

f(x) = −6(1.02)^x

x g(x)
−1 −5
0 −3
1 −1
2 1

Which equation best compares the y-intercepts of f(x) and g(x)?


a) The y-intercept of f(x) is equal to the y-intercept of g(x).
b) The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).
c) The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).
d) The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).



4) What is the value of x in the solution to the following system of equations? (5 points)

x − y = −3
x + 3y = 5

For #1 i put in 3 as the answer.
For #2 i put B as the answer.
For #3 i put B as the answer.
For #4 i put 2 as the answer.

Answer 1

All of your answers are correct, except the last one.

The last one is a system of linear equations that you can solve by using elimination:

x - y = -3

x + 3y = 5

Subtract the two equations:

-4y = -8

y = 2

Use y to solve for x:

x - (2) = -3

Add 2 to both sides:

x = -1

The answer for #4 is x = -1.

Answer 2

Answer:

1) 3

2) B

3) B

4) x=-1

Step-by-step explanation:

1) The graph of $f(x) = (0.5)^x$ is replaced by the graph of $g(x) = (0.5)^x-k.$ If g(x) is obtained by shifting f(x) down by 3 units, the value of k is 3.

2) Consider the function $f(x)=4(7)^{2x}.$ Note that $7^{2x}=(7^2)^x=49^x.$ Then

$f(x)=4\cdot 49^x.$

3) The y-intercept of f(x) is point (0,-6), because $f(0)=-6\cdot (1.02)^0=-6.$ The y-intercept of g(x) is point (0,-3). Then the y-intercept of f(x) is equal to 2 times the y-intercept of g(x).

4) From the first equation $x=y-3.$ Substitute it into the second equation:

$y-3+3y=5,\\ \\y+3y=5+3,\\ \\4y=8,\\ \\y=2.$

Then $x=2-3=-1.$