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MATH / The graph of y=f(x) is shown below.
Problem
Answer published by the source. Consult the official source to check your work against its answer.
problem
The graph of is shown below.
[asy]
unitsize(0.3 cm);
real func(real x) {
real y;
if (x >= -3 && x <= 0) {y = -2 - x;}
if (x >= 0 && x <= 2) {y = sqrt(4 - (x - 2)^2) - 2;}
if (x >= 2 && x <= 3) {y = 2*(x - 2);}
return(y);
}
int i, n;
for (i = -8; i <= 8; ++i) {
draw((i,-8)--(i,8),gray(0.7));
draw((-8,i)--(8,i),gray(0.7));
}
draw((-8,0)--(8,0),Arrows(6));
draw((0,-8)--(0,8),Arrows(6));
label("", (8,0), E);
label("", (0,8), N);
draw(graph(func,-3,3),red);
label("", (4,-3), UnFill);
[/asy]
Which is the graph of ?
[asy]
unitsize(0.3 cm);
picture[] graf;
int i, n;
real func(real x) {
real y;
if (x >= -3 && x <= 0) {y = -2 - x;}
if (x >= 0 && x <= 2) {y = sqrt(4 - (x - 2)^2) - 2;}
if (x >= 2 && x <= 3) {y = 2*(x - 2);}
return(y);
}
real funca(real x) {
return(func(2*x + 1));
}
for (n = 1; n <= 5; ++n) {
graf[n] = new picture;
for (i = -8; i <= 8; ++i) {
draw(graf[n],(i,-8)--(i,8),gray(0.7));
draw(graf[n],(-8,i)--(8,i),gray(0.7));
}
draw(graf[n],(-8,0)--(8,0),Arrows(6));
draw(graf[n],(0,-8)--(0,8),Arrows(6));
label(graf[n],"", (8,0), E);
label(graf[n],"", (0,8), N);
}
draw(graf[1],graph(funca,-2,1),red);
draw(graf[2],shift((1,0))*xscale(2)*graph(func,-3,3),red);
draw(graf[3],shift((1/2,0))*xscale(1/2)*graph(func,-3,3),red);
draw(graf[4],shift((-1,0))*xscale(1/2)*graph(func,-3,3),red);
draw(graf[5],shift((-1,0))*xscale(2)*graph(func,-3,3),red);
label(graf[1], "A", (0,-10));
label(graf[2], "B", (0,-10));
label(graf[3], "C", (0,-10));
label(graf[4], "D", (0,-10));
label(graf[5], "E", (0,-10));
add(graf[1]);
add(shift((20,0))*(graf[2]));
add(shift((40,0))*(graf[3]));
add(shift((10,-20))*(graf[4]));
add(shift((30,-20))*(graf[5]));
[/asy]
Enter the letter of the graph of
Plain-text mathematical notation (without MathML)
The graph of y=f(x) is shown below.
[asy]
unitsize(0.3 cm);
real func(real x) {
real y;
if (x >= -3 && x <= 0) {y = -2 - x;}
if (x >= 0 && x <= 2) {y = sqrt(4 - (x - 2)^2) - 2;}
if (x >= 2 && x <= 3) {y = 2*(x - 2);}
return(y);
}
int i, n;
for (i = -8; i <= 8; ++i) {
draw((i,-8)--(i,8),gray(0.7));
draw((-8,i)--(8,i),gray(0.7));
}
draw((-8,0)--(8,0),Arrows(6));
draw((0,-8)--(0,8),Arrows(6));
label("x", (8,0), E);
label("y", (0,8), N);
draw(graph(func,-3,3),red);
label("y=f(x)", (4,-3), UnFill);
[/asy]
Which is the graph of y=f(2x+1)?
[asy]
unitsize(0.3 cm);
picture[] graf;
int i, n;
real func(real x) {
real y;
if (x >= -3 && x <= 0) {y = -2 - x;}
if (x >= 0 && x <= 2) {y = sqrt(4 - (x - 2)^2) - 2;}
if (x >= 2 && x <= 3) {y = 2*(x - 2);}
return(y);
}
real funca(real x) {
return(func(2*x + 1));
}
for (n = 1; n <= 5; ++n) {
graf[n] = new picture;
for (i = -8; i <= 8; ++i) {
draw(graf[n],(i,-8)--(i,8),gray(0.7));
draw(graf[n],(-8,i)--(8,i),gray(0.7));
}
draw(graf[n],(-8,0)--(8,0),Arrows(6));
draw(graf[n],(0,-8)--(0,8),Arrows(6));
label(graf[n],"x", (8,0), E);
label(graf[n],"y", (0,8), N);
}
draw(graf[1],graph(funca,-2,1),red);
draw(graf[2],shift((1,0))*xscale(2)*graph(func,-3,3),red);
draw(graf[3],shift((1/2,0))*xscale(1/2)*graph(func,-3,3),red);
draw(graf[4],shift((-1,0))*xscale(1/2)*graph(func,-3,3),red);
draw(graf[5],shift((-1,0))*xscale(2)*graph(func,-3,3),red);
label(graf[1], "A", (0,-10));
label(graf[2], "B", (0,-10));
label(graf[3], "C", (0,-10));
label(graf[4], "D", (0,-10));
label(graf[5], "E", (0,-10));
add(graf[1]);
add(shift((20,0))*(graf[2]));
add(shift((40,0))*(graf[3]));
add(shift((10,-20))*(graf[4]));
add(shift((30,-20))*(graf[5]));
[/asy]
Enter the letter of the graph of y=f(2x+1).Original LaTeX notation
The graph of $y = f(x)$ is shown below.
[asy]
unitsize(0.3 cm);
real func(real x) {
real y;
if (x >= -3 && x <= 0) {y = -2 - x;}
if (x >= 0 && x <= 2) {y = sqrt(4 - (x - 2)^2) - 2;}
if (x >= 2 && x <= 3) {y = 2*(x - 2);}
return(y);
}
int i, n;
for (i = -8; i <= 8; ++i) {
draw((i,-8)--(i,8),gray(0.7));
draw((-8,i)--(8,i),gray(0.7));
}
draw((-8,0)--(8,0),Arrows(6));
draw((0,-8)--(0,8),Arrows(6));
label("$x$", (8,0), E);
label("$y$", (0,8), N);
draw(graph(func,-3,3),red);
label("$y = f(x)$", (4,-3), UnFill);
[/asy]
Which is the graph of $y = f(2x + 1)$?
[asy]
unitsize(0.3 cm);
picture[] graf;
int i, n;
real func(real x) {
real y;
if (x >= -3 && x <= 0) {y = -2 - x;}
if (x >= 0 && x <= 2) {y = sqrt(4 - (x - 2)^2) - 2;}
if (x >= 2 && x <= 3) {y = 2*(x - 2);}
return(y);
}
real funca(real x) {
return(func(2*x + 1));
}
for (n = 1; n <= 5; ++n) {
graf[n] = new picture;
for (i = -8; i <= 8; ++i) {
draw(graf[n],(i,-8)--(i,8),gray(0.7));
draw(graf[n],(-8,i)--(8,i),gray(0.7));
}
draw(graf[n],(-8,0)--(8,0),Arrows(6));
draw(graf[n],(0,-8)--(0,8),Arrows(6));
label(graf[n],"$x$", (8,0), E);
label(graf[n],"$y$", (0,8), N);
}
draw(graf[1],graph(funca,-2,1),red);
draw(graf[2],shift((1,0))*xscale(2)*graph(func,-3,3),red);
draw(graf[3],shift((1/2,0))*xscale(1/2)*graph(func,-3,3),red);
draw(graf[4],shift((-1,0))*xscale(1/2)*graph(func,-3,3),red);
draw(graf[5],shift((-1,0))*xscale(2)*graph(func,-3,3),red);
label(graf[1], "A", (0,-10));
label(graf[2], "B", (0,-10));
label(graf[3], "C", (0,-10));
label(graf[4], "D", (0,-10));
label(graf[5], "E", (0,-10));
add(graf[1]);
add(shift((20,0))*(graf[2]));
add(shift((40,0))*(graf[3]));
add(shift((10,-20))*(graf[4]));
add(shift((30,-20))*(graf[5]));
[/asy]
Enter the letter of the graph of $y = f(2x + 1).$level
Level 3
type
Intermediate Algebra
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