Sure! Below are sketches and descriptions of the parent functions you listed. Since I can’t create actual images, I'll describe what each graph looks like, which you could use to sketch on graph paper.
A: Linear Function
Equation: \( f(x) = x \)
Name: Linear Function
Description: The graph of this function is a straight line that passes through the origin. It has a slope of 1, meaning for every unit increase in \( x \), \( f(x) \) increases by 1. You can plot points like (-2, -2), (0, 0), and (2, 2) to illustrate the line.
B: Quadratic Function
Equation: \( f(x) = x^2 \)
Name: Quadratic Function
Description: The graph is a parabola that opens upwards. The vertex (lowest point) is at the origin (0,0). You can plot points such as (-2, 4), (-1, 1), (0, 0), (1, 1), and (2, 4) to depict the shape accurately.
C: Exponential Function
Equation: \( f(x) = 2^x \)
Name: Exponential Function
Description: The graph of this function rises sharply as \( x \) increases and approaches zero as \( x \) becomes negative. It passes through the point (0, 1) since \( 2^0 = 1 \). You can plot additional points like (-1, 0.5), (1, 2), (2, 4) to illustrate its growth.
D: Square Root Function
Equation: \( f(x) = \sqrt{x} \)
Name: Square Root Function
Description: The graph starts at the origin (0,0) and increases slowly, extending to the right in a curve. It is only defined for \( x \geq 0 \). You can plot points such as (0, 0), (1, 1), (4, 2), and (9, 3).
E: Exponential of Square Root Function
Equation: \( f(x) = 3^{\sqrt{x}} \)
Name: Exponential of Square Root Function
Description: This function also only exists for \( x \geq 0 \) and shows a rapidly increasing curve starting from \( (0, 3^0) = (0, 1) \). As \( x \) increases, the graph rises steeply. Points like (0, 1), (1, 3), (4, 9), and (9, 27) can be used to sketch this curve.
Sketching on Graph Paper
Use a piece of graph paper and:
- Label the axes (x and y).
- Mark equal intervals on both axes.
- Draw each graph according to the points plotted and label each curve with the function name and equation as specified.
Once you have created the sketches based on these descriptions, you should have a clear representation of each parent function.
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