If you vertically stretch the exponential function f(x)=2^x by a factor of 3, what is the equation of the new function
1 answer:
Answer:
Step-by-step explanation:
A vertical stretch of a function means the output values have changed by a factor of 3 or multiplication by 3. Recall, an exponential function has the basic form
.
If our equation is , then a=1. To stretch it vertically by a factor of 3, we multiply a by 3. So 1(3)=3. The value of a now becomes 3.
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We separate equation by looking at x and y projection separately.
Let us look at the x projection first.
Motion starts with initial velocity
because there is no force acting along the x-axis we don't have any acceleration along the x-axis. Our equation would be:
Now our y equation will be a little bit more complicated. There is gravity working against our projectile and we also have to take into effect the hight from which the projectile is launched.
With all that in mind let us write the equation for y projection:
The term
represents gravity and as you can see it is negative, which means gravity is pulling our projectile down.
There is one more thing we can do. We can express initial velocity
in relation to circular motion used to launch the projectile.
Where r is the length of the letter used to launch the projectile, and
is angular velocity.
If we combine our x and y equations we can get the trajectory of our projectile.
This is the equation of a parabola. If you follow this link(https://www.desmos.com/calculator/vogcuygjhs) it will take to an interactive graph where you can see how trajectory looks like depending on some of the paramaters.
Let us look at the x projection first.
Motion starts with initial velocity
Now our y equation will be a little bit more complicated. There is gravity working against our projectile and we also have to take into effect the hight from which the projectile is launched.
With all that in mind let us write the equation for y projection:
The term
There is one more thing we can do. We can express initial velocity
Where r is the length of the letter used to launch the projectile, and
If we combine our x and y equations we can get the trajectory of our projectile.
This is the equation of a parabola. If you follow this link(https://www.desmos.com/calculator/vogcuygjhs) it will take to an interactive graph where you can see how trajectory looks like depending on some of the paramaters.