Question
Fill out the table using key characteristics of linear. quadratic. and exponential functions. (1 point)
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.
Characteristic Linear Functions Quadratic Functions Exponential Functions
General Form Response area Response area Response area
Degree Response area Response area Response area
Graph Shape Response area Response area Response area
Example Equation Response area Response area Response area
Graph Response area Response area Response area
y-intercept Response area Response area Response area
x-intercept Response area Response area Response area
Domain Response area Response area Response area
Range Response area Response area Response area
Rate of Change Response area Response area Response area
Vertex Response area Response area Response area
Applications Response area Response area Response area
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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.
Characteristic Linear Functions Quadratic Functions Exponential Functions
General Form Response area Response area Response area
Degree Response area Response area Response area
Graph Shape Response area Response area Response area
Example Equation Response area Response area Response area
Graph Response area Response area Response area
y-intercept Response area Response area Response area
x-intercept Response area Response area Response area
Domain Response area Response area Response area
Range Response area Response area Response area
Rate of Change Response area Response area Response area
Vertex Response area Response area Response area
Applications Response area Response area Response area
Skip to navigation
Answers
Answered by
GPT-4o mini
Here's a filled-out table with the key characteristics of linear, quadratic, and exponential functions:
| Characteristic | Linear Functions | Quadratic Functions | Exponential Functions |
|----------------------|---------------------------------------------|---------------------------------------------|------------------------------------------------|
| General Form | \( y = mx + b \) | \( y = ax^2 + bx + c \) | \( y = a \cdot b^x \) |
| Degree | 1 | 2 | Not defined (focus on growth rate) |
| Graph Shape | Straight line | Parabola | J-shaped curve |
| Example Equation | \( y = 2x + 3 \) | \( y = x^2 - 4x + 3 \) | \( y = 3 \cdot 2^x \) |
| Graph |  |  |  |
| y-intercept | \( b \) | \( c \) | \( a \) |
| x-intercept | \( -\frac{b}{m} \) | The roots of \( ax^2 + bx + c = 0 \) | None (if \( a \), \( b > 0 \)) |
| Domain | All real numbers | All real numbers | All real numbers |
| Range | All real numbers | \( [k, \infty) \) where \( k \) is the vertex | \( (0, \infty) \) if \( a > 0 \) |
| Rate of Change | Constant \( m \) | Varies (increases/decreases) | Varies (increases exponentially) |
| Vertex | None | \( (-\frac{b}{2a}, f(-\frac{b}{2a}))\) | None |
| Applications | Constant rate of change in various fields | Projectile motion, area problems | Population growth, radioactive decay |
Feel free to adjust any item to fit your specific needs or course requirements!
| Characteristic | Linear Functions | Quadratic Functions | Exponential Functions |
|----------------------|---------------------------------------------|---------------------------------------------|------------------------------------------------|
| General Form | \( y = mx + b \) | \( y = ax^2 + bx + c \) | \( y = a \cdot b^x \) |
| Degree | 1 | 2 | Not defined (focus on growth rate) |
| Graph Shape | Straight line | Parabola | J-shaped curve |
| Example Equation | \( y = 2x + 3 \) | \( y = x^2 - 4x + 3 \) | \( y = 3 \cdot 2^x \) |
| Graph |  |  |  |
| y-intercept | \( b \) | \( c \) | \( a \) |
| x-intercept | \( -\frac{b}{m} \) | The roots of \( ax^2 + bx + c = 0 \) | None (if \( a \), \( b > 0 \)) |
| Domain | All real numbers | All real numbers | All real numbers |
| Range | All real numbers | \( [k, \infty) \) where \( k \) is the vertex | \( (0, \infty) \) if \( a > 0 \) |
| Rate of Change | Constant \( m \) | Varies (increases/decreases) | Varies (increases exponentially) |
| Vertex | None | \( (-\frac{b}{2a}, f(-\frac{b}{2a}))\) | None |
| Applications | Constant rate of change in various fields | Projectile motion, area problems | Population growth, radioactive decay |
Feel free to adjust any item to fit your specific needs or course requirements!