A mother wants to invest $6000 for her children's education. She invests a portion of the money in a bank certificate of deposit
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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
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The functions have a vertex with a x-value of 0 will be f(x) = |x|,f(x) = |x|+ 3 and f(x) = |xl - 6.Option 1,2 and 4 are functions have a vertex with a x-value of 0.
<h3>What is a function?</h3>A connection between independent variables and the dependent variable.is defined by the function. Functions help to represent graphs and equations.
The standard absolute value function is found as;
Where,
(h, k) denotes to the vertex
h is the vertex of the x-coordinate
k is the y-coordinate of the vertex
By comparing the standard equation with the given equation in the options we will get the functions to have a vertex with an x-value of 0;
The functions have a vertex with a x-value of 0 will be f(x) = |x|,f(x) = |x|+ 3 and f(x) = |xl - 6.Option 1,2 and 4 are functions have a vertex with a x-value of 0.
Hence options 1,2 and 4 are functions that have a vertex with an x-value of 0.
To learn more about the function refer to the link;