The equation of the transformation of the exponential function <em>y</em> = 2ˣ in the form <em>y</em> = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is <em>y</em> = (-2)·2ˣ + 3
<h3>What is an exponential equation?</h3>
An exponential equation is an equation that has exponents that consists of variables.
The given equation is <em>y</em> = 2ˣ
The equation for the transformation is; <em>y</em> = A·2ˣ + k
The points on the graphs are;
(0, 1), (1, -1) and (2, -5)
Plugging the <em>x </em>and <em>y</em>-values to find the value <em>A</em> and <em>k</em> gives the following simultaneous equations;
When <em>x</em> = 0, <em>y</em> = 1, therefore;
1 = A·2⁰ + k = A + k
1 = A + k...(1)
When <em>x</em> = 1, <em>y</em> = -1, which gives;
-1 = A·2¹ + k
-1 = 2·A + k...(2)
Subtracting equation (1) from equation (2) gives;
-1 - 1 = 2·A - A + k - k
-2 = A
1 = A + k, therefore;
1 = -2 + k
k = 2 + 1 = 3
k = 3
Which gives;
y = -2·2ˣ + 3 = 3 - 2·2ˣ
Learn more about the solutions to simultaneous equations here:
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131444313 oil changes in 111111 days.
3/5
Because 40/100 simplifies to 2/5 and 2/10 simplies to 1/5
1/5 + 2/5 = 3/5
Answer:
x = 3 or y = 1
Step-by-step explanation:
The line with the equation y = x + 2 passes through the point (1,3), because the coordinates of this point satisfy the equation ().
Line y = x + 2 has the slope m = 1, that means the angle between this line and positive direction of x-axis is 45°.
Thus, the line which form the angle from the line with equation y=x+2 of 45° is the vertical or horizontal line.
Vertical line has the equation x = 1, horizontal line has the equation y = 3.
Answer:
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Step-by-step explanation: