Match the parent function equation to its graph.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
y=|x|
y=x2
y=x√3
y=2x
y=x√
y=x
The parent function equations matched to their graphs are:
y=|x| - D
y=x2 - C
y=x√3 - B
y=2x - F
y=x√ - E
y=x - A
To match the parent function equations to their graphs, we can analyze the properties of each equation and compare them to the characteristics of the graph.
1. The equation y = |x| represents the absolute value function. It is a V-shaped graph where the y-values are always positive or zero.
2. The equation y = x^2 represents the quadratic function. It is a U-shaped graph that opens upwards.
3. The equation y = x√3 represents the square root function. It is a curve that starts at the origin and goes to the right.
4. The equation y = 2x represents the linear function. It is a straight line that passes through the origin.
5. The equation y = x√ represents the square root function. It is a curve that starts at the origin and goes to the right.
6. The equation y = x represents the linear function. It is a straight line that passes through the origin.
Now, let's match the corresponding equations to their graphs:
- The graph of y = |x| is a V-shaped graph with the y-values always positive or zero.
- The graph of y = x^2 is a U-shaped graph that opens upwards.
- The graph of y = x√3 is a curve that starts at the origin and goes to the right.
- The graph of y = 2x is a straight line that passes through the origin.
- The graph of y = x√ is a curve that starts at the origin and goes to the right.
- The graph of y = x is a straight line that passes through the origin.
Matched parent function equations to their graphs:
y = |x|: V-shaped graph
y = x^2: U-shaped graph
y = x√3: Curve starting at the origin and going to the right
y = 2x: Straight line passing through the origin
y = x√: Curve starting at the origin and going to the right
y = x: Straight line passing through the origin
To match the parent function equation to its graph, we need to analyze the characteristics of each equation. Let's break them down one by one:
1. y = |x|: This is the absolute value function. It takes the input "x" and outputs the absolute value of "x". The graph of this equation will be a "V" shape, with the vertex at the origin.
2. y = x^2: This is a quadratic function. It squares the input "x" to obtain the output. The graph of this equation will be a parabola opening upward.
3. y = x√3: This equation represents a linear function. It multiplies the input "x" by the constant sqrt(3) to obtain the output. The graph of this equation will be a straight line with a positive slope.
4. y = 2x: This is also a linear function. It multiplies the input "x" by 2 to obtain the output. The graph of this equation will be a straight line with a positive slope steeper than the line in equation 3.
5. y = x√: It seems there is a missing variable or constant after the square root symbol, so I am unable to determine the specific graph for this equation.
6. y = x: This is a linear function where the output is equal to the input. The graph of this equation will be a straight line with a slope of 1.
Based on the descriptions above, we can now match the parent function equation to its graph:
- The graph of equation 1 (y = |x|) will be the "V" shape.
- The graph of equation 2 (y = x^2) will be the parabola opening upward.
- The graph of equation 3 (y = x√3) will be the straight line with a positive slope.
- The graph of equation 4 (y = 2x) will be the straight line with a steeper positive slope.
- The graph of equation 5 (y = x√) is unclear without further information.
- The graph of equation 6 (y = x) will be the straight line with a slope of 1.
I hope this helps you match the parent function equations to their respective graphs!