Assume the point (3,-7) is on the graph of f(x)...

Question

What point is on the graph of: y=f(3x), y= -4(x+1), y= l f(x) l

Answer 1

Hi Brianna,

 

Given the point (3,-7) that lies on f(x), this tells you that

f(3) = -7

 

If y=f(3x),

f(3) = -7

y = f(3x) = f(3) = -7     this is true when

3x = 3

x = 1

Which gives the point

(1, -7)

 

If y = | f(x) |, then at x=3, you get

y = | f(3) |

y = | -7 |

y = 7

(3, 7)

 

If y = -4(x+1), you could plug any value in for x and determine y. Should this have been y = -4 f(x+1)? It would make more sense in context.

Answer 2

Brianna, this is a scaling and stretching of functions problem.

 

Let y=f(x) and if -7=f(3) is the original point.

 

For f(3x) indicates the function is compressed in the horizontal by a factor of 3. Hence, the new point would be (3/3,-7)=(1,-7).

 

For y=-4(x+1)=-4(3+1)=-4(4)=-16  Hence, the new point is (3,-16)

 

And y=| f(x) | =| f(3) | = |-7|=7 Hence, the new point would be (3,7)

 

Hope this helps.