Graphing Functions, Algebra 1 STAAR Prep

Graphing & Identifying Key Features of Linear, Quadratic,
& Exponential Functions + Systems & Inequalities

Using the TI-NSpire Calculator

​Slope of Graphs:

TEKS A.3A:

Determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y - y₁ = m(x - x₁).

Multiple Choice

What is the slope of the line?

• Zero

• Undefined

• 1

• -1

Multiple Choice

Find the slope of the line.

• Undefined
• 0
• 1
• -1

Multiple Choice

Find the slope, m, of the line.

$$m\ =\ \frac{rise}{run}$$

• -2
• 2
• -1
• 1

Multiple Choice

Find the slope, m, of the line.

$$m\ =\ \frac{rise}{run}$$

• 1/4
• -1/4
• -4
• 4

​Linear Functions:

TEKS A.3C:

Graph linear functions and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems.

Multiple Choice

Linear function t has an x-intercept of -1 and a y-intercept of 5.

Which graph best represents t?

Multiple Choice

Which graph best represents y = -4(x + 3) - 2?

Multiple Choice

Which graph best represents -5y = -6x + 15?

Calc. Hack: Type nsolve(-5y = -6x + 15, y) in the graphing feature and choose the matching graph.

Multiple Choice

Linear function k has a zero of -2 and a y-intercept of 6. Which graph best represents k?

Multiple Choice

The graph of linear function k passes through the points (-7, 0) and (1, 8).

Which statement must be true?

• The slope of the graph of k is $$-\frac{4}{3}$$ .

• The graph of k passes through the point (-1, -8).

• The zero of k is 7.

• The x-intercept of the graph of k is -7.

Quadratic Functions:

TEKS A.7A:

Graph quadratic functions and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry.

Multiple Choice

Two characteristics of quadratic function p are given.

1) The axis of symmetry of the graph of p is x = -3.

2) Function p has exactly one zero.

Based on this information, which graph could represent p?

Fill in the Blanks

Multiple Choice

The graph of a quadratic function is shown on the grid.

Which coordinates best represent the vertex of the graph?

• (2.4, 0)

• (0, -1)

• (-0.4, 0)

• (1, -2)

Multiple Choice

A graph of $$f\left(x\right)=6x^2-11x+3$$  is shown on the grid.

What are the zeros of f?

• 3

• 2 and 9

• $$\frac{11}{12}$$  

• $$\frac{1}{3}$$  and $$\frac{3}{2}$$  

Multiple Choice

Which graph best represents f(x) = x² - 2x - 3

Multiple Choice

Which graph best represents $$y=-x^2+6x-1$$ ?

​Exponential Functions:

TEKS A.9D:

Graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems.

Multiple Choice

The graph of an exponential function is shown on the grid. Which dashed line is an asymptote for the graph?

• Line q

• Line r

• Line s

• Line t

Multiple Choice

Which graph best represents $$f\left(x\right)=2\left(5\right)^x$$ ?

Multiple Choice

Which graph best represents $$y=10\left(0.85\right)^x$$  ?

​Systems of Equations:

TEKS A.3F

Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist.

Multiple Choice

Which system is shown on the graph?

• x - y = 4

  x + y = 2

• x + y = 4

  2x - 2y = 1

• x + y = -4

  x - y = 2

• x + y = 4

  x - y = -2

Multiple Choice

Which system is best represented by the graph?

1.) In the graphing function, type nsolve(2x + y = 1, y) and Enter. Repeat with the other equation(s). Find the matching graphs.

2.) OR plug in the point into the equations and choose the answer with 2 Trues.

• 2x + y = 1

  x - y = 2

• x + 2y = 1

  x - 2y = 2

• 2x + 2y = 1

  2x - 2y = 2

• 2x - y = 1

  x + y = 2

​Linear Inequalities:

TEKS A.3D:

Graph the solution set of linear inequalities in two variables on the coordinate plane.

Multiple Choice

Select the correct graph for each inequality.

• A
• B
• C
• D

Multiple Choice

Select the correct graph for each inequality.

• A
• B
• C
• D

Multiple Choice

Select the correct graph for each inequality.

Calc. Tip: Change the $$\ge$$ to = and graph it.

• A
• B
• C
• D

Multiple Choice

Select the correct graph for each inequality.

• A
• B
• C
• D

​Systems of Inequalities:

TEKS A.3H:

Graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Identify the graph represented by the following system of inequalities.

2x - y > 4

4x + 2y < 6