8th Grade Math Flashcards: Analyze And Sketch Function Graphs

What this deck covers

This deck focuses on Analyze And Sketch Function Graphs, giving you a quick way to review the definitions, rules, and examples that matter most for 8th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What qualitative graph matches “decreases at a constant rate”?

Answer: A straight line falling left to right (linear with $m<0$). Constant negative slope creates steady downward line.

Flashcard 2: Identify the slope sign when a graph falls from left to right.

Answer: Negative slope: $m<0$. Falling lines have negative slopes.

Flashcard 3: Identify the slope sign when a graph rises from left to right.

Answer: Positive slope: $m>0$. Rising lines have positive slopes.

Flashcard 4: What does the slope represent for a graph of $y$ versus $x$?

Answer: The rate of change: rac{ ext{change in }y}{ ext{change in }x}. Slope measures steepness and direction of change.

Flashcard 5: What graphical feature shows that a relationship is nonlinear?

Answer: The graph is not a straight line; the slope changes. Curves or bends indicate varying rates of change.

Flashcard 6: What graphical feature shows that a relationship is linear?

Answer: The graph is a straight line with constant slope. Linear means constant rate of change between any two points.

Flashcard 7: What does it mean for a function to be constant on an interval in a graph?

Answer: As $x$ changes, $y$ stays the same (a horizontal segment). Horizontal line has zero slope, so $y$ doesn't change.

Flashcard 8: What does it mean for a function to be decreasing on an interval in a graph?

Answer: As $x$ increases, $y$ decreases (the graph falls left to right). Falling graph means negative change in $y$ as $x$ grows.

Flashcard 9: What does it mean for a function to be increasing on an interval in a graph?

Answer: As $x$ increases, $y$ increases (the graph rises left to right). Rising graph means positive change in $y$ as $x$ grows.

Flashcard 10: What qualitative graph matches “increases at a constant rate”?

Answer: A straight line rising left to right (linear with $m>0$). Constant positive slope creates steady upward line.

Flashcard 11: Which interval shows the function increasing for points $(1,2)$, $(3,5)$, $(6,4)$?

Answer: Increasing on $1\le x\le 3$. $y$ goes from 2 to 5 as $x$ goes from 1 to 3.

Flashcard 12: What is the $y$-intercept on a graph, in words and notation?

Answer: The value of $y$ when $x=0$; point $(0,b)$. Where the graph crosses the vertical axis.

Flashcard 13: What is the $x$-intercept on a graph, in words and notation?

Answer: The value of $x$ when $y=0$; point $(a,0)$. Where the graph crosses the horizontal axis.

Flashcard 14: Identify the $y$-intercept of the line through $(0,-2)$ and $(3,4)$.

Answer: $y$-intercept is $-2$ (point $(0,-2)$). The line passes through $(0,-2)$.

Flashcard 15: Which interval shows the function decreasing for points $(1,2)$, $(3,5)$, $(6,4)$?

Answer: Decreasing on $3\le x\le 6$. $y$ goes from 5 to 4 as $x$ goes from 3 to 6.

Flashcard 16: Is the line through $(0,3)$ and $(4,1)$ increasing or decreasing?

Answer: Decreasing, since $m=\frac{1-3}{4-0}=-\frac{1}{2}$. Negative slope means the line falls.

Flashcard 17: Which is steeper: line $A$ with slope $2$ or line $B$ with slope $\frac{1}{2}$?

Answer: Line $A$ is steeper because $|2|>|\frac{1}{2}|$. Compare absolute values of slopes for steepness.

Flashcard 18: What qualitative graph matches “starts high, decreases quickly, then levels off”?

Answer: A decreasing curve that flattens (slope negative, $|m|$ shrinking). Rapid decrease followed by gradual leveling.

Flashcard 19: What does it mean if a graph becomes less steep (flattens) as $x$ increases?

Answer: The rate of change is decreasing; $y$ changes slower per $1$ in $x$. Flatter slope means slower rate of change.

Flashcard 20: What does it mean if a graph becomes steeper as $x$ increases?

Answer: The rate of change is increasing; $y$ changes faster per $1$ in $x$. Steeper slope means faster rate of change.

Flashcard 21: What does a slope of $0$ mean about the graph and the relationship?

Answer: The graph is horizontal; $y$ is constant as $x$ changes. No slope means no vertical change.

Flashcard 22: What does a positive slope mean about the relationship between $x$ and $y$?

Answer: Positive relationship: as $x$ increases, $y$ increases. Both variables move in the same direction.

Flashcard 23: Which option describes a linear graph: A) curve B) straight line C) zigzag with corners?

Answer: B) Straight line. Linear graphs are always straight lines.

Flashcard 24: What qualitative change occurs if a graph switches from falling to rising at one point?

Answer: It changes from decreasing to increasing at a turning point (minimum). A valley where direction reverses.

Flashcard 25: Identify the intervals of increase for a V-shape with vertex at $(0,0)$ opening upward.

Answer: Increasing for $x>0$ (and decreasing for $x<0$). V-shape rises on the right side of vertex.

Flashcard 26: Which sketch matches: increasing at a constant rate with $y$-intercept $2$?

Answer: An upward straight line crossing the $y$-axis at $(0,2)$. Constant positive slope starting at $y=2$.

Flashcard 27: Identify whether the function is increasing, decreasing, or constant from $(0,3)$ to $(4,1)$.

Answer: Decreasing (the $y$-values go from $3$ down to $1$). Compare $y$-values: $3$ to $1$ is a decrease.

Flashcard 28: What feature on a graph shows a nonlinear function?

Answer: It is not a straight line; the slope (rate of change) changes. Curves or bends indicate changing rates of change.

Flashcard 29: What feature on a graph shows a linear function (not just an interval)?

Answer: A straight line with a constant rate of change (constant slope). Linear functions have constant slope throughout.

Flashcard 30: What does a negative slope mean about the relationship between $x$ and $y$?

Answer: Negative relationship: as $x$ increases, $y$ decreases. Variables move in opposite directions.