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New YorkMaths

Algebra I: Functions and Statistics

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What does it mean for a relation to be a function, and how do you read the key features of its graph?

Understand the definition of a function and function notation; evaluate functions; identify domain and range; and interpret the key features of a graph (intercepts, intervals of increase and decrease, relative maxima and minima, and average rate of change) in context.
A NY Regents Algebra I answer on functions: the definition and the vertical-line test, function notation and evaluation, domain and range, and reading key features of a graph such as intercepts, increasing intervals, and average rate of change.
9 min answer →

How do you tell a linear model from an exponential one, and how do you build each from a context?

Distinguish linear from exponential growth (constant difference versus constant ratio), construct linear and exponential functions from descriptions, tables, or two points, and interpret their parameters (initial value, rate of change, growth factor) in context.
A NY Regents Algebra I answer on linear and exponential models: recognizing constant difference versus constant ratio, building each model from a context or table, and interpreting the slope, initial value, and growth factor.
9 min answer →

How do you summarize and compare one-variable data using center, spread, and the right display?

Represent and interpret one-variable data with dot plots, histograms, and box plots; compute and interpret measures of center (mean, median) and spread (range, interquartile range, standard deviation informally); identify outliers; and compare two distributions.
A NY Regents Algebra I answer on one-variable data: dot plots, histograms, and box plots, the mean and median, range, interquartile range and standard deviation, the 1.5 times IQR outlier rule, and comparing distributions.
9 min answer →

How do you graph a quadratic function and read its vertex, axis of symmetry, intercepts, and transformations?

Graph quadratic functions and identify key features (vertex, axis of symmetry, zeros, y-intercept, maximum or minimum); relate the three forms; and describe the effect of transformations on the parent function.
A NY Regents Algebra I answer on quadratic functions: graphing the parabola, finding the vertex and axis of symmetry, reading zeros and the y-intercept, relating standard, factored, and vertex forms, and describing transformations.
9 min answer →

How do you fit a line to two-variable data, interpret its slope and intercept, and read the correlation and residuals?

Construct and interpret scatter plots; fit a linear (or exponential) model to bivariate data; interpret the slope and intercept in context; compute and interpret residuals; and distinguish the correlation coefficient from causation.
A NY Regents Algebra I answer on bivariate data: scatter plots, fitting a line of best fit, interpreting slope and intercept, computing residuals, reading the correlation coefficient, and the correlation-versus-causation distinction.
9 min answer →