Questions: Which parent function matches the graph? f(x)=√(x) f(x)=x f(x)=∛(x) f(x)=a ⋅ b^x

Solution Steps

To determine which parent function matches the graph, we need to understand the basic shapes of the given functions:

1. \( f(x) = \sqrt{x} \) is a square root function.
2. \( f(x) = |x| \) is an absolute value function.
3. \( f(x) = \sqrt[3]{x} \) is a cube root function.
4. \( f(x) = a \cdot b^x \) is an exponential function.

We can plot these functions using Python to visually compare them with the given graph.

We need to understand the basic shapes of the given functions:

1. \( f(x) = \sqrt{x} \) is a square root function.
2. \( f(x) = |x| \) is an absolute value function.
3. \( f(x) = \sqrt[3]{x} \) is a cube root function.
4. \( f(x) = a \cdot b^x \) is an exponential function.

We plot each function over the range \([-10, 10]\) to visually compare them.

1. Square Root Function: \( f(x) = \sqrt{x} \) is defined only for \( x \geq 0 \) and has a shape that starts at the origin and increases slowly.
2. Absolute Value Function: \( f(x) = |x| \) is defined for all \( x \) and has a V-shape with a vertex at the origin.
3. Cube Root Function: \( f(x) = \sqrt[3]{x} \) is defined for all \( x \) and has an S-shape, passing through the origin.
4. Exponential Function: \( f(x) = a \cdot b^x \) is defined for all \( x \) and grows rapidly for positive \( x \).

Final Answer