Question

1.Which statement correctly describes the relationship between the graph of f(x)=4xf(x)=4x and the graph of g(x)=f(x)+3g(x)=f(x)+3 ?
a.The graph of g(x)g(x) is the graph of ​ f(x)f(x) ​ translated 3 units down ​.

b.The graph of g(x)g(x) is the graph of ​ f(x)f(x) translated 3 units left​​​.

c.The graph of g(x)g(x) is the graph of f(x)f(x) translated 3 units up.

d.The graph of g(x)g(x) is the graph of ​ f(x)f(x) translated 3 units right​​.​

2.Which statement correctly describes the relationship between the graph of f(x)f(x) and g(x)=f(x+2)g(x)=f(x+2) ?
a.The graph of g(x)g(x) is the graph of ​f(x)f(x)​ translated 2 units down.

b.The graph of g(x)g(x) is the graph of ​f(x)f(x)​ translated 2 units right.

c.The graph of g(x)g(x) is the graph of ​f(x)f(x)​ translated 2 units left.

d.The graph of g(x)g(x) is the graph of ​f(x)f(x)​ translated 2 units up.

Answer 1

Part 1:

For this case we have the following function transformation:

Vertical translations:

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

For k = 3 we have:

$g (x) = f (x) +3\\g (x) = 4x + 3$

Answer:

c.The graph of g (x) is the graph of f (x) translated 3 units up.

Part 2:

For this case we have the following function transformation:

Horizontal translations:

Suppose that h> 0

To graph y = f (x + h), move the graph of h units to the left.

For h = 2 we have:

$g (x) = f (x + 2)\\g (x) = 4 (x + 2)$

Answer:

c.The graph of g (x) is the graph of f (x) translated 2 units left.

Answer 2

1) f(x) = 4x and g(x) = f(x) + 3

Answer: the graph of g(x) is the graph of f(x) translated 3 units up.

2) g(x) = f(x+2)

Answer: the graph of g(x) is the graph of f(x) translated two units left.