AP Precalculus Flashcards: Function Model Construction And Application

What this deck covers

This deck focuses on Function Model Construction And Application, giving you a quick way to review the definitions, rules, and examples that matter most for AP Precalculus.

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 is the equation of the horizontal line at y=4?

Answer: $y = 4$. Horizontal line has constant y-value for all x.

Flashcard 2: What is the inverse function of $f(x) = \frac{1}{x}$?

Answer: $f^{-1}(x) = \frac{1}{x}$. Function is its own inverse (self-inverse).

Flashcard 3: Identify the transformation: $f(x) = 2x^2$.

Answer: Vertical stretch by a factor of 2. Coefficient 2 multiplies all y-values, stretching vertically.

Flashcard 4: What is the general form of a cubic function?

Answer: $f(x) = ax^3 + bx^2 + cx + d$. Highest degree term $ax^3$ with lower degree terms.

Flashcard 5: What is the y-intercept of $f(x) = -5x + 10$?

Answer: $y = 10$. Evaluate $f(0)$ to find where graph crosses y-axis.

Flashcard 6: Find the x-intercept of $f(x) = 2x - 4$.

Answer: $x = 2$. Set $f(x) = 0$ and solve: $2x - 4 = 0$.

Flashcard 7: What is the y-intercept of the function $f(x) = 3x^2 + 2x + 1$?

Answer: $y = 1$. Evaluate $f(0) = 3(0)^2 + 2(0) + 1 = 1$.

Flashcard 8: Identify the parent function of $f(x) = x^2$.

Answer: Quadratic function. Basic parabola opening upward.

Flashcard 9: State the equation of a circle in standard form.

Answer: $(x-h)^2 + (y-k)^2 = r^2$. Center at $(h,k)$ with radius $r$.

Flashcard 10: Find the amplitude of $f(x) = 3\text{sin}(x)$.

Answer: Amplitude is 3. Coefficient determines maximum displacement from center.

Flashcard 11: Identify the transformation: $f(x) = (x-3)^2$.

Answer: Horizontal shift right by 3 units. Subtracting inside parentheses shifts graph right.

Flashcard 12: What is the effect of $f(x) = \frac{1}{2}x$ on the graph?

Answer: Vertical compression by a factor of $\frac{1}{2}$. Coefficient $\frac{1}{2}$ reduces all y-values by half.

Flashcard 13: State the domain of the square root function.

Answer: All non-negative real numbers. Cannot take square root of negative numbers in real domain.

Flashcard 14: What is the effect of $f(x) = x^2 + 5$ on the graph?

Answer: Vertical shift up by 5 units. Adding constant moves entire graph upward.

Flashcard 15: What is the range of the logarithmic function $f(x) = \text{log}(x)$?

Answer: All real numbers. Logarithm can output any real number value.

Flashcard 16: What is the effect of $f(x) = -x^2$ on the graph?

Answer: Reflection over the x-axis. Negative coefficient flips parabola upside down.

Flashcard 17: Identify the axis of symmetry for $f(x) = x^2 - 4x + 3$.

Answer: $x = 2$. Use formula $x = -\frac{b}{2a} = -\frac{-4}{2(1)} = 2$.

Flashcard 18: State the range of the cosine function.

Answer: From -1 to 1 inclusive. Cosine oscillates between minimum -1 and maximum 1.

Flashcard 19: What is the effect of $f(x) = \text{sin}(x) - 1$?

Answer: Vertical shift down by 1 unit. Subtracting constant moves entire graph downward.

Flashcard 20: Identify the transformation: $f(x) = \frac{1}{x+2}$.

Answer: Horizontal shift left by 2 units. Adding inside parentheses shifts graph left.

Flashcard 21: What is the range of $f(x) = e^x$?

Answer: All positive real numbers. Exponential function always produces positive outputs.

Flashcard 22: Find the range of the function $f(x) = 3x + 7$.

Answer: All real numbers. Linear functions have unlimited output values.

Flashcard 23: Identify the function type: $f(x) = \frac{1}{x}$.

Answer: Rational function. Ratio of polynomials defines rational functions.

Flashcard 24: Find the domain of $f(x) = \frac{1}{x-2}$.

Answer: All real numbers except $x = 2$. Denominator cannot equal zero, so $x \neq 2$.

Flashcard 25: Find the zeros of $f(x) = x^2 - 4$.

Answer: $x = 2, x = -2$. Set $f(x) = 0$: $x^2 - 4 = 0$, so $x^2 = 4$.

Flashcard 26: What is the general form of a linear function?

Answer: $f(x) = mx + b$. Standard slope-intercept form where $m$ is slope and $b$ is y-intercept.

Flashcard 27: What is the standard form of a quadratic function?

Answer: $f(x) = ax^2 + bx + c$. Standard form with leading coefficient $a$, linear term $bx$, and constant $c$.

Flashcard 28: Identify the vertex form of a quadratic function.

Answer: $f(x) = a(x-h)^2 + k$. Shows vertex at $(h,k)$ with $a$ controlling width and direction.

Flashcard 29: Find the slope of the line $2x - 3y = 6$.

Answer: Slope $m = \frac{2}{3}$. Rearrange to $y = \frac{2}{3}x - 2$ form.

Flashcard 30: Which function represents exponential growth?

Answer: $f(x) = a \times b^x$ where $b > 1$. Base $b > 1$ ensures growth; $a$ is initial value.

Flashcard 31: What is the period of $f(x) = \text{sin}(2x)$?

Answer: $\frac{\text{Period}}{2}$. Coefficient of $x$ doubles frequency, halving period to $\pi$.

Flashcard 32: Find the inverse of $f(x) = 2x + 3$.

Answer: $f^{-1}(x) = \frac{x-3}{2}$. Switch variables and solve: $x = 2y + 3$ gives $y = \frac{x-3}{2}$.

Flashcard 33: What is the domain of $f(x) = \text{log}(x)$?

Answer: All positive real numbers. Logarithm undefined for zero and negative inputs.

Flashcard 34: Find the vertex of $f(x) = (x-1)^2 + 3$.

Answer: Vertex at $(1, 3)$. Vertex form directly shows vertex coordinates $(h,k)$.