I am having issues with f(x)

[RickyJames]

The graph of [FONT=MathJax_Math]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT]contains the point [FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]7[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Main])[/FONT]. What point must be on each of the following transformed graphs? Enter points as [FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]a[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math]b[/FONT][FONT=MathJax_Main])[/FONT] including the parentheses.
(a) The graph of [FONT=MathJax_Math]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]8[/FONT][FONT=MathJax_Main])[/FONT] must contain the point
(b) The graph of [FONT=MathJax_Math]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]6[/FONT] must contain the point
(c) The graph of [FONT=MathJax_Math]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]5[/FONT] must contain the point


I tried for a: (-1,4),(7,-4),(-1,-4)
b1,4)
c14,4)

Thanks for your help

 

[Otis]

I added three words to a sentence, and the system reformatted my post into a single paragraph, removing boldface.

The graph of f(x)contains the point (7,4). What point must be on each of the following transformed graphs? Enter points as (a,b) including the parentheses. (a) The graph of f(x−8) must contain the point (b) The graph of f(x)−6 must contain the point (c) The graph of f(x+2)+5 must contain the point I tried for a: (-1,4) ... b: (1,4) c: (14,4)

Hi! I'm reading the question like this: Where does the original point (7,4) end up, on each of the transformed graphs? For your answer above to (a), it looks like you shifted in the wrong direction. If c is a positive number, the graph of f(x-c) is the same as the graph of f(x) shifted c units horizontally to the right. The graph of f(x+c) is the same as the graph of f(x) shifted c units horizontally to the left. This may be backwards, from what you'd expect, so you just have to memorize the facts. For your answer to (b), you did a horizontal shift when you ought to have done a vertical shift. f(x) + c shifts the graph of f(x) up c units if c is positive and down c units if c is negative. Note the difference here: f(x+c) and f(x)+c When some number c is added (or subtracted) to x, the shift is horizontal; when c is added (or subtracted) to f(x), the shift is vertical. For your answer to (c), you applied both shifts horizontally (and, in the wrong direction). Part (c) has both a horizontal shift and a vertical shift because both x and f(x) are being changed. The horizontal shift will be two units because it's x that's being changed by 2. What direction will this horizontal shift be? The vertical shift will be five units because it's f(x) that's being changed by 5. What direction will this vertical shift be? If you're still confused, let us know, and we'll post some examples (or links to examples). Cheers

 

[Ishuda]

The graph of [FONT=MathJax_Math]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT]contains the point [FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]7[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Main])[/FONT]. What point must be on each of the following transformed graphs? Enter points as [FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]a[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math]b[/FONT][FONT=MathJax_Main])[/FONT] including the parentheses.
(a) The graph of [FONT=MathJax_Math]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]8[/FONT][FONT=MathJax_Main])[/FONT] must contain the point
(b) The graph of [FONT=MathJax_Math]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]6[/FONT] must contain the point
(c) The graph of [FONT=MathJax_Math]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]5[/FONT] must contain the point


I tried for a: (-1,4),(7,-4),(-1,-4)
b1,4)
c14,4)

Thanks for your help

What do you know about f(x)? Well you know f(7)=4, so what is x when
(a) f(x-8) = f(7)
(b) f(x) = f(7)
(c) f(x+2) = f(7)
Given that then compute the rest. For example consider f(x+14)+10:
f(-7+14) + 10 = f(7) + 10 = 4 + 10 = 14
so (-7, 14) would be on the graph of f(x+14)+10.[FONT=MathJax_Main][/FONT]

 

[RickyJames]

I completed the problem thank you everyone for your help