Question

Consider the functions
f(x) = 4 sin(πx)
g(x) = 4 sin(πx) − 1
Which statement best describes the relationship between the graphs of f(x) and g(x)?
1. g is a vertical shift of f upward by 1
units.
2. g is a horizontal shift of f to the left by 1
units.
3. g is a vertical shift of f downward by 1
units.
4. None of these.

5. g is a horizontal shift of f to the right by
1 units

Answer 1

Vertical shift downward by 1

Answer 2

These are really easy

Answer 3

i dont understand! explain please

Answer 4

Hmmm, I'm not good at explaining things

Answer 5

Basically, it's the graph of the function at every point except you shift it down by -1 at every point

Answer 6

So ultimately the whole f(x) shifts down by -1 all at the same time when you graph it

Answer 7

Thus creating g(x)

Answer 8

so if it is +1 then it shift upward?

Answer 9

yes, if +1 is outside the parentheses

Answer 10

how do you know if its vertical or horizontal?

Answer 11

think about a list of numbers, inputs and outputs. in the first you put in a bunch of numbers, get out a bunch of numbers. in the second you put in the same numbers, get out the same numbers and then subtract 1. so outputs are all one less than they used to be. that shifts everything down one unit

Answer 12

so if i have
\[f(x)\] and
\[f(x)+3\] i know
\[f(x)+3\] is identical to f(x) except shifted up three units

Answer 13

ooh very simple

Answer 14

yes it is simple. it is a bit different when you compare
\[f(x)\text { and } f(x+2)\] however

Answer 15

in this case you add two before you evaluate the function. this has the effect of shifting the graph HORIZONTALLY two units LEFT

Answer 16

compare
\[f(x)=x^2\] with
\[f(x)=(x+2)^2\] and you will see why it is shifted left

Answer 17

ok this one is shifting horizontally but not upward nor downward