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WARRIOR [948]
2 years ago
13

I just need help with question one, but if you want to you can answer question 2 as well. I’ll give 100 points!

Mathematics
2 answers:
valentinak56 [21]2 years ago
6 0

Answer:

<u>Translations</u>

For a > 0

f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}

f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}

f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}

f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}

y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a

y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}

y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}

y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}

<h3><u>Question 1</u></h3>

Given:  f(x)=(2,-3)

f(x)+2 \implies (x, y+2)= (2,-3+2)=(2,-1)

f(x)-3 \implies (x,y-3)=(2,-3-3)=(2,-6)

f(x+5)\implies (x-5,y)=(2-5,-3)=(-3,-3)

-f(x) \implies (x,-y)=(2,-(-3))=(2,3)

f(-x) \implies (-x,y)=(-(2),-3)=(-2,-3)

f(2x) \implies \left(\dfrac{x}{2},y\right)=\left(\dfrac{2}{2},-3\right)=(1,-3)

2f(x) \implies (x,2y)=(2,2 \cdot -3)=(2,-6)

-f(x-4) \implies (x+4,-y)=(2+4,-(-3))=(6,3)

\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & &\\f(x)+2 & f(x)-3 & f(x+5) & -f(x) & f(-x) & f(2x) & 2f(x) & -f(x-4)\\& & & & & & &\\\cline{1-8} & & & & & & &\\(2,-1) & (2,-6) & (-3,-3) & (2,3) & (-2,-3) & (1,-3) & (2,-6) & (6,3)\\& & & & & & &\\\cline{1-8} \end{array}

<h3><u>Question 2</u></h3>

Parent function:  y=x^2

Given function:  f(x)=(x+8)^2-4

f(x+8) \implies f(x) \: \textsf{translated}\:8\:\textsf{units left}

f(x)-4 \implies f(x) \: \textsf{translated}\:4\:\textsf{units down}

Therefore, <u>a translation 8 units to the left and 4 units down.</u>

adoni [48]2 years ago
4 0

Explanation:

Given f(x) : (2, -3)

<h3>Translation's:</h3>

f(x) + 2 then graph <u>translates up by 2 units up</u> =  \boxed{\sf (2, -1)}

f(x) - 3 then graph <u>translates down 3 units down</u> = \boxed{\sf (2, -6)}

f(x + 5) then graph <u>translates left 5 units</u> = \boxed{\sf (-3, -3)}

-f(x) then graph <u>reflects over x axis</u> = \sf \boxed{\sf (2, 3)}

f(-x)  then graph <u>reflects over y axis</u> = \sf \boxed{\sf (-2,-3)}

f(2x) then graph has <u>horizontal compression</u> = (2/2, -3) = \boxed{\sf (1, -3)}

2f(x) then graph has <u>vertical compression</u> = (2, (-3)2) = \boxed{\sf (2, -6)}

-f(x - 4) then graph r<u>eflects over x axis</u>, <u>moves 4 units to right</u> = \sf \boxed{\sf (6, 3)}

<h3><u>Solution 2</u></h3>

Parent function: y = x²

Graph function: f(x) = (x + 8)² - 4

After Identification:

D. The graph has a translation of 8 units left and 4 units down.

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