pls I need some math help

[Allupyourfinger]

Write the equation for the function that results from each transformation applied to the base function y=2^x

 

 

Reflect with respect to the y-axis, right 5, down 3, verticle compression of 1/2

[CodeNova]

17 minutes ago, Allupyourfinger said:

Write the equation for the function that results from each transformation applied to the base function y=2^x 

 

 

Reflect with respect to the y-axis, right 5, down 3, verticle compression of 1/2

y=((2^(x-2))-3)/2

maybe? I haven't taken a math class in years.

[Dash Lambda]

This looks like a homework problem. I'll explain what you're doing at each step using an arbitrary function f(x).

 

Reflection about the y-axis: You're flipping the direction of the x-axis, so f(x) -> f(-x).

Translate 5 to the right: You're moving it along the x-axis, which means you're changing x again, so f(x) -> f(x - 5).

Translate 3 down: Now you're moving it along the y-axis, which means you're modifying y, and the function itself is your y coordinate, so f(x) -> f(x) - 3.

Compress vertically by 1/2: You're squishing the function so it's half as tall, so f(x) -> f(x)/2

[Allupyourfinger]

7 hours ago, Dash Lambda said:

This looks like a homework problem. I'll explain what you're doing at each step using an arbitrary function f(x).

 

Reflection about the y-axis: You're flipping the direction of the x-axis, so f(x) -> f(-x).

Translate 5 to the right: You're moving it along the x-axis, which means you're changing x again, so f(x) -> f(x - 5).

Translate 3 down: Now you're moving it along the y-axis, which means you're modifying y, and the function itself is your y coordinate, so f(x) -> f(x) - 3.

Compress vertically by 1/2: You're squishing the function so it's half as tall, so f(x) -> f(x)/2

[r2724r16]

10 hours ago, Allupyourfinger said:

Write the equation for the function that results from each transformation applied to the base function y=2^x

Reflect with respect to the y-axis, right 5, down 3, verticle compression of 1/2

The equation is f(x) = 1/2(2)^-(x-5) -3

 

Steps:

- f(x) = 2^x

- f(-x) = 2^-(x)

- f[-(x-5)] = 2^-(x-5)

- f[-(x-5)] -3 = 2^-(x-5) -3

- 1/2f[-(x-5)] -3 = 1/2(2)^-(x-5) -3

[r2724r16]

10 hours ago, CodeNova said:

y=((2^(x-2))-3)/2

maybe? I haven't taken a math class in years.

That's not correct.

8 hours ago, Dash Lambda said:

Reflection about the y-axis: You're flipping the direction of the x-axis, so f(x) -> f(-x).

Translate 5 to the right: You're moving it along the x-axis, which means you're changing x again, so f(x) -> f(x - 5).

Translate 3 down: Now you're moving it along the y-axis, which means you're modifying y, and the function itself is your y coordinate, so f(x) -> f(x) - 3.

Compress vertically by 1/2: You're squishing the function so it's half as tall, so f(x) -> f(x)/2

OP wants the equation for the function.

 

Also for the vertical compression, it's more correct to write 1/2f(x) than f(x)/2.

[Dash Lambda]

1 hour ago, Geography said:

OP wants the equation for the function.

I said it looked like a homework problem.

I love to help people with math, but I make a habit of not just telling them the end result, instead telling them how to get the end result. If someone's having trouble understanding how to do something, giving them enough of the reasoning behind it for them to do it themselves is infinitely more helpful than telling them the answer.

 

1 hour ago, Geography said:

Also for the vertical compression, it's more correct to write 1/2f(x) than f(x)/2.

Actually, that's somewhat ambiguous notation. You would ideally write (1/2)f(x) or f(x)/2, as 1/2f(x) does not rigorously enforce whether the function is in the numerator or denominator.

Neither way is more correct, though. They're the same exact thing; f(x)/2 is just (1/2)f(x) after you've performed the multiplication. It's like the difference between f(x) + (-3) and f(x) - 3.

[r2724r16]

9 hours ago, Dash Lambda said:

If someone's having trouble understanding how to do something, giving them enough of the reasoning behind it for them to do it themselves is infinitely more helpful than telling them the answer.

Obviously it is. Even I mentioned the steps. But I also wrote the answer, which is what the OP wanted.

9 hours ago, Dash Lambda said:

Actually, that's somewhat ambiguous notation.

It's difficult to write fractions in this forum since you'll need brackets in so many places.

9 hours ago, Dash Lambda said:

They're the same exact thing; f(x)/2 is just (1/2)f(x) after you've performed the multiplication.

The Canadian education system taught me that (1/2)f(x) is more correct.

[Dash Lambda]

23 minutes ago, Geography said:

Obviously it is. Even I mentioned the steps. But I also wrote the answer, which is what the OP wanted.

But if you give people the answers, they don't have to do it themselves. My priorities are often different from simply answering questions.

 

30 minutes ago, Geography said:

It's difficult to write fractions in this forum since you'll need brackets in so many places.

Which is why I don't. Or at least, why I avoid it.

 

31 minutes ago, Geography said:

The Canadian education system taught me that (1/2)f(x) is more correct.

Yeah... That's kind'a the problem with compulsory education systems nowadays, they get so pedantic. Especially with math.

 

Another thing is having radicals in the denominator. There's nothing wrong with it, it's just sometimes easier to work with if you get them out -but kids are taught to always get the radicals out of the denominator, even if it just wastes time and doesn't make anything easier.