Types of Functions in Algebra 1 (Part 2 of 5)

Types of Functions in Algebra 1 (Part 2 of 5)

In this part, we will focus on the graphs and equations of the functions.

Linear Functions

• When graphed, they always form a line.

• Equations of linear functions are degree one (and on special occasions, degree zero.)

• We call horizontal lines (degree zero) constant functions and most consider them to be special linear functions.

Multiple Select

Which of the following are graphs of linear equations?

Multiple Select

Which of the following are graphs of linear equations?

Multiple Select

Which of the following are graphs of linear equations?

Multiple Select

Which of the following are graphs of linear equations?

Linear Functions

• When graphed, they always form a line.

• Equations of linear functions are degree one (and on special occasions, degree zero.)

• We call horizontal lines (degree zero) constant functions and most consider them to be special linear functions.

Multiple Select

Which of the following functions represent linear functions?

• $f\left(x\right)=x+3$

• $f\left(x\right)=5^x-2$

• $f\left(x\right)=2x^2-3x+5$

• $f\left(x\right)=7$

• $f\left(x\right)=19x\ -\ 5\ +\ 2x$

Multiple Select

Which of the following functions represent linear functions?

•  $f\left(x\right)=-2\left(x-1\right)^2+8$ 

•  $f\left(x\right)=-232$ 

•  $f\left(x\right)=5x^1-3$ 

•  $f\left(x\right)=-\left|x-3\right|+8$ 

Multiple Select

Which of the following functions represent linear functions?

•  $f\left(x\right)=-2\left(x-1\right)^2+8$ 

•  $f\left(x\right)=7\left(x-3\right)+8\left(x+2\right)$ 

•  $f\left(x\right)=5^x+2$ 

•  $f\left(x\right)=2x^1+7x^1-8x^0$ 

Multiple Select

Which of the following functions represent linear functions?

•  $f\left(x\right)=-2\left(x-1\right)^2+8$ 

•  $f\left(x\right)=2\left|x\right|+7$ 

•  $f\left(x\right)=2\left(3\right)^x-1$ 

•  $f\left(x\right)=5$ 

•  $f\left(x\right)=3-x$ 

Quadratic Functions

• Graph is in the shape of a parabola (which looks like a hill or a valley)

• Equation is always degree two.

Quadratic Functions

• Graph is in the shape of a parabola (which looks like a hill or a valley)

• Equation is always degree two.

Multiple Select

Which of the following are graphs of quadratic functions?

Multiple Select

Which of the following are graphs of quadratic functions?

Multiple Select

Which of the following are graphs of quadratic functions?

Multiple Select

Which of the following are graphs of quadratic functions?

Quadratic Functions

• Graph is in the shape of a parabola (which looks like a hill or a valley)

• Equation is always degree two.

Multiple Select

Which of the following functions represent quadratic functions?

• $f\left(x\right)=x+3$

• $f\left(x\right)=5^x-2$

• $f\left(x\right)=2x^2-3x+5$

• $f\left(x\right)=7$

• $f\left(x\right)=19x\ -\ 5\ +\ 2x$

Multiple Select

Which of the following functions represent quadratic functions?

•  $f\left(x\right)=-2\left(x+5\right)^2-13$ 

•  $f\left(x\right)=-232$ 

•  $f\left(x\right)=5x^1-3$ 

•  $f\left(x\right)=-\left|x-3\right|+8$ 

Multiple Select

Which of the following functions represent quadratic functions?

•  $f\left(x\right)=-2\left(x-1\right)^2+8$ 

•  $f\left(x\right)=7\left(x-3\right)+8\left(x+2\right)$ 

•  $f\left(x\right)=5^x+2$ 

•  $f\left(x\right)=2x^2+7x^1-8x^0$ 

Multiple Select

Which of the following functions represent quadratic functions?

•  $f\left(x\right)=5-x^2$ 

•  $f\left(x\right)=2\left|x\right|+7$ 

•  $f\left(x\right)=2\left(3\right)^x-1$ 

•  $f\left(x\right)=5$ 

•  $f\left(x\right)=3-x$ 

Exponential Functions

• Graph is a flat and flare.

• You can recognize the equations because the variable is in the exponent.

Exponential Functions

• Graph is a flat and flare.

• You can recognize the equations because the variable is in the exponent.

Multiple Select

Which of the following are graphs of exponential functions?

Multiple Select

Which of the following are graphs of exponential equations?

Multiple Select

Which of the following are graphs of exponential functions?

Multiple Select

Which of the following are graphs of exponential functions?

Exponential Functions

• Graph is a flat and flare.

• You can recognize the equations because the variable is in the exponent.

Multiple Select

Which of the following functions represent exponential functions?

• $f\left(x\right)=x+3$

• $f\left(x\right)=5^x-2$

• $f\left(x\right)=2x^2-3x+5$

•  $f\left(x\right)=7^x$ 

• $f\left(x\right)=19x\ -\ 5\ +\ 2x$

Multiple Select

Which of the following functions represent exponential functions?

•  $f\left(x\right)=2\left(x+5\right)^2-13$ 

•  $f\left(x\right)=-223$ 

•  $f\left(x\right)=2\left(0.25\right)^{\left(3x-1\right)}+8$ 

•  $f\left(x\right)=-3^x$ 

Multiple Select

Which of the following functions represent exponential functions?

•  $f\left(x\right)=-2\left(x-1\right)^2+8$ 

•  $f\left(x\right)=7\left(x-3\right)+8\left(x+2\right)$ 

•  $f\left(x\right)=7\left(0.3\right)^x+2$ 

•  $f\left(x\right)=2x^2+7x-8$ 

Multiple Select

Which of the following functions represent exponential functions?

•  $f\left(x\right)=5-x^2$ 

•  $f\left(x\right)=2\left|x\right|+7$ 

•  $f\left(x\right)=5$ 

•  $f\left(x\right)=2\cdot3^x-1$ 

•  $f\left(x\right)=3-x$  

What type of function?

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