GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A financial analyst is comparing two investment options. Investment A offers a fixed annual return, while Investment B's return depends on market volatility. The growth of Investment A is represented by a straight line on a graph, and Investment B's growth is represented by a curve that initially rises slowly and then more rapidly. What type of function would best describe Investment B's growth?
- AExponential function
- BQuadratic function
- CLinear function
- DConstant function
Show answer & explanationAnswer & explanation
Correct answer: A. Exponential function
A curve that initially rises slowly and then more rapidly is characteristic of exponential growth. Linear functions are straight lines, quadratic functions form parabolas, and constant functions are horizontal lines.
Why the other options are wrong
- B. A quadratic function would form a parabola, which can rise rapidly but typically has a symmetrical shape or a turning point not described here.
- C. A linear function would be a straight line, representing a constant rate of return, not a curve that rises increasingly rapidly.
- D. A constant function would show no change, a horizontal line, which contradicts the described growth.
Graphical Representation of Functions
The graph of a function visually depicts the relationship between input and output values. Different types of functions (linear, quadratic, exponential) have distinct graphical shapes.
- Linear: Straight line (constant rate of change).
- Quadratic: Parabola (rate of change is linear).
- Exponential: Curve with increasing (growth) or decreasing (decay) steepness.
- Constant: Horizontal line (zero rate of change).
Memory trick: Linear is 'Line', Quadratic is 'Curve', Exponential 'Explodes'!