Which equations have a leading coefficient of 3 and a constant term of –2? Check all that apply.
2 answers:
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<h2>Exponential Functions</h2>
Exponential functions are typically organized in this format:
To find the equation given the graph of an exponential function:
- Identify the horizontal asymptote
⇒ <em>asymptote</em> - a line towards which a graph appears to travel but never meets
⇒ If the horizontal asymptote is not equal to 0, we add this at the end of the function equation. - Identify the y-intercept
⇒ This is our <em>a</em> value. - Identify a point on the graph and solve for <em>c</em>
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<h2>Solving the Question</h2>Identify the horizontal asymptote
In this question, it appears to be x = 0.
Identify the y-intercept
The y-intercept is the value of <em>y</em> at which the graph appears to cross the y-axis. In this graph, it appears to be 100. This is our <em>a</em> value. Plug this into :
Solve for <em>c</em>
We can use any point that falls on the graph for this step. For instance, (1,50) appears to be a valid point. Plug this into our equation and solve for <em>c</em>:
Plug <em>c</em> back into our original equation: