Which of the following equations would change the y-intercept of the exponential function from (0, 1) to (0, −3)
?(1 point)
Responses
y = 4(3^x)
y = 2 (−3x)
y = −3 (2^x)
y = −1 (3^x)
The correct equation would be:
y = −1 (3^x)
To change the y-intercept of an exponential function from (0, 1) to (0, -3), we need to find the equation that translates the function vertically by 4 units downwards.
The y-intercept represents the value of y when x is 0. So, we can substitute x = 0 into each equation and check which one gives y = -3.
Let's substitute x = 0 into each equation:
1. For y = 4(3^x):
y = 4(3^0) = 4(1) = 4
2. For y = 2(-3x):
y = 2(-3*0) = 2(0) = 0
3. For y = -3(2^x):
y = -3(2^0) = -3(1) = -3
4. For y = -1(3^x):
y = -1(3^0) = -1(1) = -1
From the above calculations, we can see that only the equation y = -3(2^x) gives a y-value of -3 when x is 0. Therefore, the equation that would change the y-intercept of the exponential function from (0, 1) to (0, -3) is y = -3(2^x).
To change the y-intercept of an exponential function, you need to modify the constant term in the equation. The y-intercept occurs when x = 0, so you need to find the equation that gives a y-value of -3 when x = 0.
Let's analyze each equation given:
1. y = 4(3^x) does not change the y-intercept to (0, -3) because when x = 0, the equation becomes y = 4(3^0) = 4, not -3.
2. y = 2(-3x) is a linear equation, not an exponential function. It does not have a y-intercept, as it is not in the form y = mx + b where b represents the y-intercept.
3. y = -3(2^x) changes the y-intercept to (0, -3) because when x = 0, the equation becomes y = -3(2^0) = -3.
4. y = -1(3^x) does not change the y-intercept to (0, -3) because when x = 0, the equation becomes y = -1(3^0) = -1, not -3.
Therefore, the equation that changes the y-intercept to (0, -3) is y = -3(2^x).