Evaluating Functions

Vocabulary practice cards covering algebraic and graphical evaluation of functions, as well as solving for input values given specific function outputs.

Evaluating Functions

The mathematical process of determining the output value $f(x)$ for a given input value of $x$, or solving for the input variable $x$ given a specified output value.

$f(-1)$ given $f(x) = x^2 - 8x - 12$

$-3$, calculated by substituting $x = -1$ into the expression: $f(-1) = (-1)^2 - 8(-1) - 12 = 1 + 8 - 12 = -3$.

$f(5)$ given $f(x) = -4x + 20$

$0$, calculated by substituting $x = 5$ into the expression: $f(5) = -4(5) + 20 = -20 + 20 = 0$.

$f(-12)$ given $f(x) = \frac{2}{3}x + 7$

$-1$, calculated by substituting $x = -12$ into the expression: $f(-12) = \frac{2}{3}(-12) + 7 = -8 + 7 = -1$.

$f(7)$ given $f(x) = |9 - 2x|$

$5$, calculated by evaluating the absolute value expression: $f(7) = |9 - 2(7)| = |9 - 14| = |-5| = 5$.

$f(-4)$ given $f(x) = 2x^2 + x - 10$

$18$, calculated by substituting $x = -4$ into the expression: $f(-4) = 2(-4)^2 + (-4) - 10 = 2(16) - 4 - 10 = 32 - 14 = 18$.

$f(-2)$ given $f(x) = x^3 + 4x$

$-16$, calculated by substituting $x = -2$ into the expression: $f(-2) = (-2)^3 + 4(-2) = -8 - 8 = -16$.

$f(6)$ given $f(x) = 15 - \frac{5}{2}x$

$0$, calculated by substituting $x = 6$ into the expression: $f(6) = 15 - \frac{5}{2}(6) = 15 - 15 = 0$.

$f(-8)$ given $f(x) = |-20 - x^2|$

$84$, calculated by evaluating the absolute value expression: $f(-8) = |-20 - (-8)^2| = |-20 - 64| = |-84| = 84$.

$f(3)$ given $f(x) = -5x^2 + 20$

$-25$, calculated by substituting $x = 3$ into the expression: $f(3) = -5(3)^2 + 20 = -5(9) + 20 = -45 + 20 = -25$.

$f(7)$ given $f(x) = -x^2 + 5x + 13$

$-1$, calculated by substituting $x = 7$ into the expression: $f(7) = -(7)^2 + 5(7) + 13 = -49 + 35 + 13 = -1$.

Value of $x$ when $f(x) = -61$ for $f(x) = -3x - 7$

$x = 18$, determined by setting the function equal to $-61$: $-61 = -3x - 7 \rightarrow -54 = -3x \rightarrow x = 18$.

Value of $x$ when $f(x) = 20$ for $f(x) = 14 - 2x$

$x = -3$, determined by setting the function equal to $20$: $20 = 14 - 2x \rightarrow 6 = -2x \rightarrow x = -3$.

Value of $x$ when $f(x) = 29$ for $f(x) = \frac{x - 26}{2}$

$x = 84$, determined by setting the function equal to $29$: $29 = \frac{x - 26}{2} \rightarrow 58 = x - 26 \rightarrow x = 84$.

Value of $x$ when $f(x) = 5$ for $f(x) = -x - 11$

$x = -16$, determined by setting the function equal to $5$: $5 = -x - 11 \rightarrow 16 = -x \rightarrow x = -16$.

Value of $x$ when $f(x) = -\frac{7}{2}$ for $f(x) = \frac{1}{4}x - 8$

$x = 18$, determined by setting the function equal to $-\frac{7}{2}$: $-\frac{7}{2} = \frac{1}{4}x - 8 \rightarrow \frac{9}{2} = \frac{1}{4}x \rightarrow x = 18$.

Value of $x$ when $f(x) = -139$ for $f(x) = 8x + 61$

$x = -25$, determined by setting the function equal to $-139$: $-139 = 8x + 61 \rightarrow -200 = 8x \rightarrow x = -25$.

Value of $x$ when $f(x) = -14$ for $f(x) = 3x - 29$

$x = 5$, determined by setting the function equal to $-14$: $-14 = 3x - 29 \rightarrow 15 = 3x \rightarrow x = 5$.

Value of $x$ when $f(x) = -2$ for $f(x) = -\frac{3}{5}x - 17$

$x = -25$, determined by setting the function equal to $-2$: $-2 = -\frac{3}{5}x - 17 \rightarrow 15 = -\frac{3}{5}x \rightarrow x = -25$.

Value of $x$ when $f(x) = -25$ for $f(x) = -11 - \frac{1}{6}x$

$x = 84$, determined by setting the function equal to $-25$: $-25 = -11 - \frac{1}{6}x \rightarrow -14 = -\frac{1}{6}x \rightarrow x = 84$.

Value of $x$ when $f(x) = 89$ for $f(x) = -5x + 9$

$x = -16$, determined by setting the function equal to $89$: $89 = -5x + 9 \rightarrow 80 = -5x \rightarrow x = -16$.

Value of $f(-4)$ from the graph of $f(x)$ (Card U)

$-3$, found by locating $x = -4$ on the horizontal axis and finding the corresponding vertical coordinate on the line.

Value of $f(2)$ from the graph of $f(x)$ (Card V)

$0$, found by locating $x = 2$ on the horizontal axis where the parabolic curve crosses the horizontal $x$-axis.

Value of $x$ when $f(x) = 4$ from the graph of $f(x)$ (Card W)

$x = -1$, found by locating $4$ on the vertical $f(x)$-axis and identifying the corresponding horizontal coordinate on the line.

Value of $x$ when $f(x) = -3$ from the graph of $f(x)$ (Card X)

$x = 0$, found by locating $-3$ on the vertical $f(x)$-axis where the curve intersects the vertical axis.